physics.flu-dyn

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physics.flu-dyn 2026-05-14 2 theorems

Neglected terms grow important for heat transfer at low Prandtl numbers

Influence of Prandtl number on heat transfer over a permeable wall

Simulations at Pr down to 0.05 show these interface corrections become comparable to main transport terms, unlike at Pr=0.71.

abstract click to expand

The work considers a fully turbulent flow with heat transfer in a channel half-filled with an array of cubes based on the work of Breugem and Boersma (2005) and Chandesris et al. (2013), at $\mathrm{Re}_\mathrm{bulk} = 5485$ and three different Prandtl numbers, $\mathrm{Pr} = 0.71, 0.1, 0.05$. The temperature is modelled as a passive scalar and two different boundary condition configurations are simulated. The influence of the Prandtl number on the mean temperature, its variance and the terms of the temperature budget is highlighted, including the analysis of the distribution and relative importance of the turbulent heat transfer, molecular diffusion, tortuosity and Brinkman terms near the porous-fluid interface. The latter two has been found to be insignificant for the highest $\mathrm{Pr}$. A set of terms, typically neglected during the upscaling procedure (related to the Taylor expansion of the filtered variables), is analysed for the first time for the turbulent heat transfer at the porous-fluid interface, and are found to be significant at low $\mathrm{Pr}$. The upscaled fields are evaluated with three different kernels forming cellular average, linear (i.e., tent kernel), quadratic and cubic, and the influence of the chosen filter is additionally studied.

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physics.flu-dyn 2026-05-13 Recognition

Realizability filters cut turbulence model costs by 42%

Realizability-Constrained Machine Learning for Turbulence Closures in Wake Flows

Barycentric-map constraints inside CFD-driven gene expression programming produce stable closures that generalize across wake geometries.

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Computational fluid dynamics (CFD)-driven machine learning frameworks based on symbolic regression offer a promising pathway for turbulence model discovery, but are often hindered by numerical instability, residual stagnation, and non-physical model behavior during training. In particular, realizability, which is rarely enforced explicitly during model development, remains a critical yet overlooked requirement, especially for accurate wake prediction. In this work, a residual- and realizability-filtered CFD-driven framework is proposed to enhance both efficiency and robustness within a gene expression programming (GEP) paradigm. The method integrates two residual-based filtering criteria along with a barycentric-map-based realizability constraint directly into the CFD solution loop, enabling early identification and rejection of unstable and non-realizable candidate models. This reduces unnecessary computational effort while guiding the search toward physically admissible solutions. The proposed approach achieves a 42.3% reduction in computational cost relative to the baseline CFD-driven GEP framework and reduces non-realizable models at convergence from 58.4% to 1.7%. The framework is trained on a canonical cylinder wake. The resulting models enhance mean wake prediction and remain realizable across training and test cases, with robust generalization to diverse geometries and operating conditions, including a rectangular cylinder, an airfoil, and an axisymmetric body. The study further provides insights into realizable model statistics, coefficient trends, and conditions governing physically consistent wake behavior. These results demonstrate that incorporating realizability and stability constraints within CFD-driven learning enables efficient and physically consistent turbulence model discovery, offering a scalable pathway toward reliable data-driven closure development.

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physics.flu-dyn 2026-05-13 Recognition

Time decay selects capillary waves ahead of pressure forcing

Interfacial waves from pressure forcing: revisiting classical theories from an IVP perspective

An initial-value problem shows algebraically decaying transients cause asymmetric Fourier cancellation, yielding short waves in front and

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A localised overpressure translating at a uniform speed greater than a critical value acts at the interface between two deep fluid layers with different densities. We analyse the resulting wave patterns using an initial-value problem formulation within the linearised, inviscid, potential flow framework. The steady-state interface exhibits short capillary waves ahead of the forcing and long gravity waves behind it, arising from an asymmetric cancellation of Fourier components in the far field. The time-dependent part of the solution, decaying algebraically with time, plays a crucial role in this mechanism. This contrasts with classical steady approaches, which require additional conditions to select a unique solution. We extend this approach to a two-fluid interface and validate the predictions against nonlinear simulations.

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physics.flu-dyn 2026-05-13 Recognition

Structured analysis locates oblique turbulent band wavelength

Structured input-output analysis of oblique turbulent bands in Waleffe flow

The response strength grows as Reynolds number to the 1.7 power and matches large-domain simulation results.

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This work employs structured input-output analysis (SIOA) to study Waleffe flow. The SIOA framework employs structured uncertainty to include the componentwise structure of nonlinearity in Navier-Stokes equations, and SIOA quantifies the flow response using structured singular values. The structured input-output analysis identifies the wavelength and inclination angle of oblique turbulent bands observed in large-domain direct numerical simulations. The structured input-output response scales over Reynolds number as $\sim Re^{1.7}$.

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physics.flu-dyn 2026-05-13 2 theorems

Adaptive fluxes preserve scalar bounds in high-order flow simulations

Formulations for scalar boundedness in simulations of turbulent compressible multi-component flows using high-order finite-difference methods

New finite-difference formulations keep species mass fractions physical in under-resolved turbulent multi-component cases without preset min

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Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order, low-dissipation numerical schemes poses challenges in highly under-resolved conditions due to inherent dispersion errors that generate spurious oscillations. Numerical dissipation is needed to mitigate these oscillations, but excessive dissipation negatively affects resolution. In this work, we propose formulations for high-order finite-difference schemes to preserve scalar boundedness without predefined bounds, while maintaining high accuracy and low numerical dissipation. The proposed formulations augment a non-dissipative numerical flux of a high-order central-difference scheme with an explicit dissipative numerical flux that adaptively switches between high-order and low-order formulations. Building on a deliberate choice of the non-dissipative flux, we construct two schemes using Jameson's artificial viscosity method and a monotonicity-preserving limiter as the dissipative flux. We examine the schemes in one-dimensional scalar advection problems and a three-dimensional temporal turbulent mixing-layer case involving sharp scalar gradients and under-resolved conditions, evaluating their accuracy, boundedness of species mass fractions, and numerical diffusivity. The scheme with the monotonicity-preserving limiter demonstrates superior performance.

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physics.flu-dyn 2026-05-13 2 theorems

Intermittency forms connected conduits boosting mobility in porous media

Intermittent two-phase flow in porous media: insights from pore-scale direct numerical simulation

Pore-scale DNS shows switching pathways couple across the network, shifting pressure scaling from linear to sub-linear and raising overall (

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Recent X-ray imaging experiments have revealed that multiphase flow through porous media involves transient fluctuations in local occupancy, even under fixed macroscopic steady-state conditions where capillary forces dominate at the pore scale. To examine how intermittency manifests at the pore scale we perform direct numerical finite volume simulations (DNS) of immiscible two-phase flow through a micro-CT-derived Bentheimer sandstone geometry at capillary numbers in the Darcy and intermittent flow regimes. We show that intermittent disconnection and reconnection are accompanied by strongly coupled local pressure redistribution and non-wetting phase flow. This behaviour contrasts with the Darcy flow regime, in which the phases remain predominantly in fixed pathways. Macroscopically the computed pressure-gradient-capillary-number relationship ($\nabla P$-Ca) recovers both the linear Darcy and the sub-linear intermittent scaling regimes consistent with previous experimental measurements. We show how an increase in intermittency leads to the transition from the linear to the sub-linear regime. Using topology-aware snap-off detection, we show that the spatial extent of intermittency increases with capillary number. Spectral, local-geometry, and network-connectivity analyses provide further evidence that the intermittent elements organise into connected conduits embedded within a stable backbone of fixed flow pathways: intermittency is a network-coupled rather than purely local process. This work characterises the pore-scale manifestation of intermittency as a periodic sequence of drainage and imbibition displacements triggered by local pressure fluctuations whose macroscopic consequence is to improve the overall mobility of the fluid phases.

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physics.flu-dyn 2026-05-13 Recognition

Bayesian optimization cuts drag on high-lift wing by 9.7 percent

High-lift Wing Separation Control via Bayesian Optimization and Deep Reinforcement Learning

Open-loop search over steady jets raises efficiency 10.9 percent at constant lift while reinforcement learning gains little at Re 450000.

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This study investigates active flow control (AFC) of a 30P30N high-lift wing at a Reynolds number Re$_c$ = 450,000 and angle of attack $\alpha$ = 23$^\circ$ using wallresolved large-eddy simulations (LES). Two optimization strategies are explored: open-loop Bayesian optimization (BO) and closed-loop deep reinforcement learning (DRL), both targeting the mitigation of stall and the improvement of aerodynamic efficiency via synthetic jets on the slat, main, and flap elements. The uncontrolled configuration was validated against literature data, confirming the reliability of the LES setup. The BO framework successfully identified steady jet velocities that increased efficiency by +10.9% through a -9.7% drag reduction while maintaining lift. In contrast, the DRL agent, despite leveraging instantaneous flow information from distributed sensors, achieved only minor improvements in lift and drag, with negligible efficiency gain. Training analysis indicated that the penalty-dominated reward constrained exploration. These results highlight the need for carefully designed rewards and computational acceleration strategies in DRL-based flow control at high Reynolds numbers.

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physics.flu-dyn 2026-05-13 2 theorems

Nonlinear Schlieren maps steep liquid surfaces accurately

Nonlinear synthetic Schlieren methods for free-surface topography measurement using telecentric imaging

Telecentric optics and iterative solvers extend precise elevation measurements to high-slope and high-amplitude waves

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Free-surface synthetic Schlieren (FS-SS) is a high-resolution, refraction-based optical technique for measuring the instantaneous elevation of a liquid interface. Under the assumptions of small amplitude, small slope, and small paraxial angle, the method yields a linear relationship between the gradient of the surface elevation and the apparent displacement field of a refracted pattern imaged through the surface. Here, we propose three new, nonlinear extensions of the FS-SS method that are specifically dedicated to telecentric imaging. Paraxial distortions are eliminated with a telecentric lens, thereby simplifying the optical model. This allows us to derive nonlinear surface reconstruction models that reach beyond the usual limits of small slope and small wave-magnitudes. We implement these nonlinear surface reconstruction algorithms and compare them to the original, linear reconstruction algorithm in three different experiments, using a solid glass lens, spreading oil drops and nonlinear Faraday waves. At the price of a few iterations, we can realise nonlinear surface reconstructions that are more precise, in particular when we reach high slopes or high amplitude regimes. We share a library that encodes these nonlinear surface reconstruction algorithms.

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physics.flu-dyn 2026-05-13 1 theorem

Shear layer at cavity makes waves that break into bubbles

Air entrainment by an inclined smooth water jet

Inclined jets entrain air because uneven flow detachment along the impact cavity generates an unstable wavefield.

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Air entrainment can occur when a water jet impacts a water/air interface, a process central in various real systems, ranging from dam spills to breaking waves. Despite its prevalence, a comprehensive description of the mechanism controlling bubble size distribution remains elusive. Here, we establish a link between the geometry and the dynamics of the cavity observed when an inclined impinging jet impacts a water interface and the resulting bubble cloud. We show that the bubbles result from the destabilization of the wavefield developing at the interface of the cavity. The origin of this wave field is the creation of a shear layer, due to the asymmetric detachment of the flow field from the interface.

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physics.flu-dyn 2026-05-13 Recognition

Block-coupled method stabilizes polymer mixing simulations in extruders

A Volume of Fluid Immersed Boundary Method for Industrial Polymer Mixing

Integrating VOF and immersed boundary with implicit viscous coupling yields consistent velocity and pressure fields in partially filled extr

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This work develops advanced numerical methods for free-surface simulations of polymer mixing processes, integrating a Volume of Fluid (VOF) interface-capturing approach with a non-conforming Immersed Boundary (IB) method to model two-phase flows of highly viscous polymer melts and air within partially filled rotating mixing devices, implemented within the Finite Volume OpenFOAM library. To overcome severe numerical instabilities arising from the strong viscosity contrast between polymer melts and air, a block-coupled scheme providing fully implicit viscous diffusion treatment is integrated into the VOF-IB framework, relaxing time-step stability constraints and substantially reducing computational cost with respect to standard segregated solvers. The resulting BC-VOF-IB solver is applied to industrially relevant geometries of single- and twin-screw extruders, yielding physically consistent predictions of velocity and pressure fields under partial filling conditions. While further developments, most notably the inclusion of thermal effects, remain necessary, the proposed framework represents a meaningful step toward bridging academic CFD research and the practical demands of industrial polymer processing.

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physics.flu-dyn 2026-05-13 2 theorems

Mutual information yields parameter-free SGS models

Information-Preserving SGS model based on the local inter-scale equilibrium hypothesis

Maximizing information between turbulence scales sets parameters without empirical tuning and matches prior accuracy.

abstract click to expand

Large eddy simulation has been widely used to simulate turbulence at balanced computational cost and accuracy. Many Subgrid-Scale (SGS) models have been proposed over the years, where data-driven and machine learning-aided approaches set the recent trend. To address the problem of extrapolation in these models, we propose a new data-driven SGS model based on an information-theoretic picture of turbulence. To this end, we estimate the model parameters by maximizing mutual information, which correspond to the scale-by-scale local equilibrium hypothesis in developed turbulence or "information preservation." An a priori test confirmed that the estimated parameters are in good agreement with the previously reported empirical values. Furthermore, a posteriori tests on periodic box turbulence and channel turbulence exhibited accuracy comparable to the existing models. These results suggest the utility of the information-theoretic picture of turbulence for constructing more generic SGS models without the need for empirically prescribed model parameters, while enhancing physical interpretability beyond black-box approaches.

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physics.flu-dyn 2026-05-13 2 theorems

Energy balance closes unified law for maximum drop spreading

Kinematic Closure of Drop Impact

Time and velocity taken directly from energy balance multiply to give maximum diameter that fits all data without regime switches.

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Existing models for droplet impact prescribe the spreading contact time and effective spreading velocity from asymptotic arguments, which prevents a self-consistent prediction of the maximum spreading ratio across regimes. Here, the total spreading time and characteristic spreading velocity are derived directly from the energy balance, with explicit capillary and viscous contributions. Multiplying this time and velocity to obtain the maximum spreading diameter yields a closed, unified scaling law for the maximum spreading ratio of wetting drops across inertio-capillary and inertio-viscous regimes. The resulting expression quantitatively collapses the present measurements and literature data over wide ranges of Weber and Ohnesorge numbers, droplet sizes, and surface wettabilities without prefactors that need to be adjusted to a certain regime.

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physics.flu-dyn 2026-05-13 2 theorems

Neural primitive reconstructs continuous 3D flame fields

Neural Refractive Index Primitives for Flame Field Reconstruction Using Background-Oriented Schlieren

Hash-encoded multilayer perceptron with gradient losses recovers turbulence from schlieren data better than voxel or frequency methods.

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An improved neural refractive-index-primitive method for background-oriented schlieren tomography is presented, enabling continuous three-dimensional reconstruction of refractive-index fields using a compact multilayer perceptron. The method adopts the refractive-index field as the sole neural primitive and integrates multiresolution hash encoding, automatic-discrete gradient losses, and a three-dimensional mask to enable fast convergence and high-resolution, spatially coherent reconstructions. Tests on numerical combustion phantoms and real flame data demonstrate accurate recovery of both large-scale structures and fine-scale turbulence, strong robustness to noise, and clear advantages over frequency-encoding-based and voxel-based reconstruction methods.

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physics.flu-dyn 2026-05-12 2 theorems

GPR generalizes Green's integration for noisy pressure data

Pressure reconstruction from error-embedded gradient measurements: a Gaussian-process generalization of Green's function integration

It eliminates boundary conditions, supplies uncertainty estimates, and matches or beats traditional accuracy on turbulence data.

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Reconstructing scalar fields from error-embedded gradient measurements is a fundamental linear inverse problem with broad applications in computational physics. Conventional approaches, such as Poisson-based solvers and the Green's Function Integration (GFI) method, require explicit boundary conditions extracted from the same error-embedded observations. In this study we assess the accuracy of a Gaussian Process Regression (GPR) framework for reconstructing pressure fields in turbulent flows from error-embedded pressure-gradient data derived from kinematic measurements. The probabilistic nature of GPR inherently provides tunable denoising, eliminates the need for boundary conditions, and produces a pointwise posterior-variance error estimate. A central theoretical result of the present work is that GFI is the noiseless limit of GPR, which on the unbounded plane reduces to the well-known logarithmic kernel and in three dimensions to the inverse-distance kernel. The framework is validated on two-dimensional slices and three-dimensional subdomains of a forced homogeneous isotropic turbulence from the Johns Hopkins Turbulence Database. With an empirical mixture-of-Gaussians (MoG-$3$) kernel fitted directly to the pressure correlation function, GPR performs at least as well as GFI. In situations with under-resolved data or high noise, GPR outperforms GFI, while delivering a calibrated pointwise posterior uncertainty whose standardized residuals satisfy $|z|<2$ over $95\%$ of grid points. The framework extends to three dimensions through a tensor-product Kronecker solver coupled to conjugate gradients with close to $\mathcal{O}(N^3\log N)$ cost. A closed-form error lower bound on a periodic cube is derived for the GPR operator, with the residual gap attributable to boundary contamination on non-periodic finite domains.

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physics.flu-dyn 2026-05-12 2 theorems

Blade strain precedes wake velocity in turbine model

Cross-correlating blade--wake dynamics for a model wind turbine

Negative lags in cross-correlations point to blades actively shaping downstream wakes, key for fatigue prediction in wind farms.

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Understanding how wakes interact with wind turbine blades under varying operating and inflow conditions is essential for improving fatigue prediction and performance assessment in increasingly dense wind farms. We present an experimental investigation of wake-blade coupling in a model wind turbine, focusing on the role of tip-speed ratio, $\lambda$, under varying free-stream turbulence conditions. Spatially resolved wake velocity measurements are acquired concurrently with distributed blade strain measurements using Rayleigh backscattering fibre-optic sensing, enabling direct, time-synchronised analysis of fluid-structure interaction across the blade's span. The blades' strain dynamics are strongly governed by $\lambda$, where variations of the operating condition of the turbine modify the amplitude, coherence, and the temporal/spectral organisation of the blade's structural dynamics, while free-stream turbulence primarily modulates these responses. Instantaneous joint statistics reveal negligible zero-lag dependence between wake velocity and blade strain, motivating a lagged and frequency-resolved analysis. Cycle-averaged cross-correlation and cross-power spectral density analyses demonstrate that wake-induced blade response is spatially localised within the wake shear layers and organised around rotation-coherent frequencies, with the coupling strength peaking at intermediate downstream locations. These results highlight the dominant role of operating condition in shaping wake-mediated blade loading and demonstrate the value of concurrent, spatially resolved flow-structure measurements for resolving blade-exciting flow dynamics in wind-turbine wakes. Furthermore, a consistent negative-lag peak indicates that blade strain fluctuations systematically precede downstream wake velocity fluctuations, suggesting a causal, blade-driven imprint on the wake.

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physics.flu-dyn 2026-05-12 Recognition

Droplet coalescence diagram measures viscosity and surface tension

Dripping-onto-droplet capillary breakup

Filament breakup time in dripping-onto-droplet setup maps to Ohnesorge and Bond numbers for regime identification and property measurement.

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This experimental, numerical, and theoretical study investigates the capillary thinning and breakup of Newtonian filaments formed following the coalescence of a millimetric-nozzle-generated pendant drop with a lower droplet cap contained in a millimetric cylinder in ambient air, i.e., dripping-onto-droplet capillary breakup (DoD). Our mixed approach combines filament breakup experiments recorded with a high-speed camera and three-dimensional numerical simulations based on a variational multiscale framework for multiphase fluid flows. The results are analysed by considering the dynamics of fluid filament thinning, energy transfers, and scaling laws. Three flow regimes are highlighted: capillary-inertial, capillary-viscous, and mixed capillary-inertial-viscous. All regimes are affected by gravity. The findings are summarised in a two-dimensional diagram that correlates the filament breakup time with different flow regimes using the important dimensionless parameters of the problem, e.g., the Ohnesorge number (which relates the viscous stress to inertial and capillary stresses) and the Bond number (which balances the gravitational stress with the capillary one). This diagram can be used to quantify both the liquid viscosity and the liquid-gas surface tension (for Newtonian fluids). Lastly, we demonstrate that DoD can also be used as a rheometric test, giving access to the extensional relaxation time of polymer solutions (for viscoelastic fluids).

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physics.flu-dyn 2026-05-11 2 theorems

Reduced equations predict rare transitions in active fluids

Rare transitions between collective states in an active fluid via a weakly nonlinear reduction

Stochastic amplitude equations match full simulations for noise-driven switches between two stable collective states at far lower cost.

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We study a model for a dilute suspension of rod-like particles swimming at constant velocity in a Stokes flow. As the translational diffusivity of the particles decreases, a two-dimensional uniform concentration of randomly aligned particles undergoes either a codimension-2 pitchfork bifurcation or a codimension-4 Hopf bifurcation, depending on the particles' swimming speed. We use a weakly nonlinear expansion to reduce the system to a low-dimensional one for the amplitudes of the bifurcating eigenmodes. The originality of our calculations lies in incorporating spatio-temporal white noise forcing. The stochastic forcing terms in the amplitude equations are derived analytically from the noise acting on the original system. Past the onset of the bifurcations, the particles deterministically self-organize into steady or oscillating states of collective motion. For the Hopf bifurcation scenario, two stable periodic orbits are found to coexist, each corresponding to a distinct collective dynamics. The stochastic forcing induces rare transitions between them. Owing to the low dimensionality of amplitude equations, steady and dynamical statistics can be computed directly from the Fokker-Planck equation, or via the Adaptive Multilevel Splitting (AMS) rare-event algorithm. In particular, extremely long mean transition times and associated out-of-equilibrium paths between the periodic orbits are obtained. These paths can be understood in light of the invariant manifolds of the low-dimensional system, which brings insights into the mechanism behind the transitions. We also performed fully nonlinear stochastic simulations and used the AMS algorithm directly on the full system. The statistics are in good quantitative agreement with those computed on the reduced systems, the latter being obtained at a considerably lower numerical cost.

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physics.flu-dyn 2026-05-11 2 theorems

Mack-mode forcing alone triggers full turbulent cascade in SWBLI

Optimal non-linear mechanisms for laminar-turbulent transition of a shock-induced separated shear layer

Optimal structures stay quasi-invariant from small to transitional amplitudes and outline a four-stage path through vortices and streaks.

abstract click to expand

Laminar-turbulent transition in shock wave-boundary-layer interactions (SWBLI) remains a major challenge for hypersonic vehicle design, with implications for drag, heat transfer, and structural loads. Linear optimal perturbation analyses can identify candidate instabilities, but the full route to breakdown in SWBLI requires nonlinear optimisation. Here, we characterise the optimal transition pathway in a globally stable yet convectively unstable Mach 2.15 oblique SWBLI using a nonlinear input-output optimisation framework based on the space-time spectral Navier-Stokes formulation of Poulain et al. (Comput. Fluids, 2024). The nonlinear frequency-domain approach captures mean-flow distortion, resolves triadic energy transfers, and extracts intrinsic nonlinear stresses that activate additional instability mechanisms. We identify a four-stage pathway: (1) optimal forcing of oblique first Mack mode waves at moderate frequencies; (2) nonlinear self-interaction of counter-propagating Mack waves, generating streamwise Gortler-like vortices in the reattachment region where streamline curvature peaks; (3) lift-up of streamwise velocity streaks by these vortices; and (4) subharmonic sinuous secondary instability leading to streak breakdown. Optimisation across forcing amplitudes from infinitesimal to transitional levels yields quasi-invariant optimal forcing structures, showing that exciting the oblique first Mack mode alone can trigger the turbulent cascade. Parametric studies over frequency-wavenumber space and forcing configurations confirm this preferential pathway. By resolving nonlinear energy transfers with a finite number of harmonics, this work provides a tractable framework for transition prediction and control strategy development in high-speed separated flows, bridging linear stability theory and fully turbulent simulation.

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physics.flu-dyn 2026-05-11 2 theorems

Elasticity shrinks critical size for acoustic particle trapping

Viscoelastic control of acoustic particle migration and trapping in microchannels

In microchannels the Deborah number lowers the particle radius where radiation forces beat streaming drag, enabling submicron control.

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Particle migration and trapping in ultrasonically actuated microscale flows arise from the competition between acoustic radiation forces and streaming-induced drag. While these mechanisms are well understood in Newtonian fluids, the role of fluid viscoelasticity in governing particle dynamics remains largely unexplored. Here, we investigate particle transport and trapping in a viscoelastic fluid within an ultrasonically excited microchannel under the combined action of acoustic streaming and radiation forces. Using a perturbation framework, we solve the continuity, momentum and constitutive equations for an Oldroyd-B fluid to obtain the oscillatory acoustic field and the resulting steady streaming flows in the bulk and near-wall boundary layers. Acoustic radiation forces, incorporated through a semi-analytical model, drives particle migration, while streaming-induced drag can oppose, alter or suppress trapping. We show that particle trajectories and equilibrium trapping locations are governed primarily by the Deborah number ($De$) and viscous diffusion number ($Dv$). At high $Dv$, increasing $De$ shifts the trapping location from the bulk region to the channel wall, pressure nodal line, channel centre or ultrasound symmetry line. We further determine the critical particle size governing the transition between radiation-dominated and streaming-dominated regimes as a function of $De$ and $Dv$. The critical particle size can become significantly smaller than that in a Newtonian fluid, enabling effective manipulation of submicron particles and overcoming a key limitation of conventional acoustofluidics. These results demonstrate how viscoelasticity fundamentally modifies acoustophoretic transport and establish new mechanisms for tunable particle migration and trapping in complex fluids.

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physics.flu-dyn 2026-05-11 2 theorems

Symbolic closure from two flows generalizes to channel turbulence in LBM

Data-driven Symbolic Closure for Turbulence Modeling in the Lattice Boltzmann Framework

Fitted without wall terms, the model matches dissipation peaks and secondary vortices better than the Smagorinsky approach.

abstract click to expand

Turbulence modeling within the Lattice Boltzmann Method (LBM) framework has long relied on traditional algebraic sub-grid scale (SGS) models, which often suffer from over-dissipation and lack of spatial selectivity near solid boundaries. In this work, we utilize Physical Symbolic Optimization (Phi-SO) to discover explicit analytical closures from high-fidelity DNS datasets of Taylor-Green Vortex (TGV) and Lid-Driven Cavity (LDC) flows. Central to our methodology is the integration of virtual dimensional analysis and non-linear tensor invariants, a strategy that enforces physical scaling laws directly within the symbolic search process. The resulting model exhibits a highly non-linear dependency on both strain-rate and rotation-rate invariants. Numerical validations confirm that this symbolic closure outperforms the standard Smagorinsky approach in capturing kinetic energy dissipation rate peaks and resolving delicate secondary corner vortices. Furthermore, the model exhibits robust zero-shot generalization to wall-bounded turbulent channel flow (Re_tau = 180) without the aid of any supplemental wall-damping corrections. This work highlights the potential of symbolic regression to uncover robust, interpretable physical laws for the next generation of intelligent computational fluid dynamics solvers.

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physics.flu-dyn 2026-05-11 2 theorems

Swirl-switching in pipe bends is local instability

Disentangling coherent structures and the origin of swirl-switching

Decomposition reveals bend and downstream structures have different origins, with bend mode matching mean-flow instability.

abstract click to expand

Modal decomposition of turbulent flows using classical proper orthogonal decomposition (POD) often suffers from mode mixing, in which a distinct coherent structure may be distributed over several POD modes. We propose a decomposition method based on the Hilbert transform and band-pass filtering to address this issue (filtered Hilbert POD -- FHPOD). We apply this approach to the turbulent flow through a 180 bent pipe at $Re_D=10,000$ (based on bulk velocity ($U_b$) and pipe diameter ($D$)) and curvature $\gamma=0.2$, simulated using direct numerical simulation. The FHPOD results in four distinct mode families, including a swirl-switching mode at Strouhal number of 0.13 localised in the curved section. Our novel modal decomposition shows that the modes observed in the bend and downstream correspond to distinct physical mechanisms rather than to a single universal swirl-switching instability throughout the pipe, as previous work implied. To further examine the origin of the swirl-switching mode, we perform a local stability analysis of the cross-sectional mean flow along the bend. We find unstable eigenmodes at the same streamwise wavenumber and within the same range of Strouhal numbers as the swirl-switching mode found in the modal decomposition. The result supports the interpretation that the swirl-switching phenomenon is an intrinsic instability of the curved-pipe flow that can be excited and potentially enhanced by incoming turbulent structures, but is ultimately not caused by them. Finally, we also establish a link of the downstream modes to the local shear layers of the modified base flow, highlighting the different nature of these modes.

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physics.flu-dyn 2026-05-11 Recognition

Bent straw turns dyed water into observable vortex rings

A bent straw as a tool for an affordable student-safe experiment in vortex ring dynamics

Students control parameters and record secondary structures plus mirroring with only a phone camera and basic measurements.

abstract click to expand

Vortex dynamics are an important topic in fluid dynamics, explaining phenomena like drag and lift generation, jet propulsion, and corner flows. It is also often excluded from introductory or undergraduate fluid dynamics courses on account of its complexity and the inaccessibility of practical and engaging experiments. We present an affordable student-safe experiment to generate vortex rings and study their dynamics using a bent straw and dyed water that allows students to control key parameters, can be imaged using a smartphone camera, and explains the complex physics with simple and easily measured parameters. Vortex rings are produced that parallel seminal experiments, demonstrating secondary structures and the mirroring effect. Meanwhile, nonplanar and triangular jet exits are used to demonstrate asymmetric vortex rings and vortex ring inversion.

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physics.flu-dyn 2026-05-11 2 theorems

Ultrasound triggers self-similar microjets in vaporizing droplets

Bubble jetting in acoustic microdroplet vaporization

Multiple bubble nucleation inside microdroplets creates complex pressures that drive piercing jets with possible use in cell-targeted drug交付

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Acoustic droplet vaporization denotes the phase-change of micron- and sub-micron-sized droplets upon the application of high-amplitude ultrasound. The asymmetric collapse of the incepted vapor bubbles within the droplets can give rise to high-speed liquid microjets. Here, we describe acoustically-driven and bubble-pair jetting arising within the vaporizing droplet, observed experimentally with ultra-high-speed imaging at the microscale. The existence of complex pressure fields due to the continued acoustic wave-droplet interaction and the nucleation of multiple bubbles within the droplet leads to rich dynamics, with the jets presenting behavioral self-similarity to millimetric bubbles under comparable conditions. Evaporative instabilities that develop during bubble growth impede jet formation during bubble collapse. Furthermore, the ability of the jets to pierce the droplet interface and penetrate into the surrounding fluid is discussed. These powerful microjets could be harnessed to induce cell permeabilization for targeted drug delivery and treatment of cancerous tissue.

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physics.flu-dyn 2026-05-11 2 theorems

Timing parameter predicts vortex ring formation in bubble collisions

Vortex ring formation from the interaction of a cavitation bubble with a confined air bubble: experiments and a timing criterion

Experiments show a dimensionless value between 1 and 1.5 separates liquid-slug impacts that create rings from those that do not.

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We study vortex ring formation arising from the interaction between a cavitation bubble and a confined air bubble in a cylindrical blind hole, using high-speed shadowgraphy imaging. As the cavitation bubble grows above the hole, it drives a downward flow that compresses the air bubble at the base. The air bubble subsequently expands, expelling the overlying liquid column upward as a coherent slug; impact of this slug on the far boundary of the collapsing cavitation bubble produces a vortex ring. Parametric experiments across the dimensionless stand-off distance $\mathcal{H} = h/R_{\max}$ and the air bubble fill fraction $\mathcal{B} = (d_\text{hole} - d_\text{top})/d_\text{hole}$ identify three regimes: (i) liquid column impact during collapse, producing a vortex ring ($\mathcal{H} \lesssim 0.5$, $\mathcal{B} \lesssim 0.5$); (ii) late impact near the end of collapse (large $\mathcal{H}$); and (iii) direct air bubble impact after bypassing the liquid column (large $\mathcal{B}$), with neither (ii) nor (iii) producing a ring. Two one-dimensional models, based on the Rayleigh-Plesset equation and isentropic air bubble expansion, predict the liquid column impact location and its speed $U_\text{lc}$, respectively. A dimensionless timing parameter $\Pi = (h + R_{\max}) / (U_\text{lc} \cdot t_\text{cav}/2)$, comparing the liquid column travel time to the cavitation collapse half-period, distinguishes the three regimes: ring formation occurs for $1 \lesssim \Pi \lesssim 1.5$. The ring propagates from the hole at an initial speed of $5$ m/s, decelerating quadratically, and breaks apart via azimuthal instabilities at $Re \approx 4500$.

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physics.flu-dyn 2026-05-11 1 theorem

Wavy films make droplet impacts asymmetric

Species Transport Driven by Droplet Impact in Wavy Thin Films

Local depth gradients redirect cavity flows and create uneven mixing until inertial forces at higher speeds restore symmetric behavior.

abstract click to expand

Droplet impact on thin liquid films is commonly studied on quiescent surfaces, although practical systems often involve residual capillary waves generated by preceding droplets. This study examines how such traveling waves modify impact dynamics and mixing. Controlled surface disturbances were produced using an acoustic excitation system that replicated droplet-induced waves, and a two-color laser-induced fluorescence method was implemented to obtain simultaneous measurements of film thickness and dye concentration. Impacts on wavy films deviated markedly from quiescent conditions. Rim evolution, cavity collapse, and jet formation became asymmetric, governed by the phase of the wave relative to the impact. These behaviors were linked to local variations in film depth, which redirected cavity retraction and the associated mixing flow. Reconstructed concentration fields confirmed that droplet liquid is displaced according to these depth gradients, producing asymmetric mixing at moderate Weber numbers. A dimensionless asymmetry index quantified the dependence on wave amplitude, phase, and distance from the acoustic wave generator. At higher Weber numbers, inertial mixing attenuated these effects, and the dynamics approached those of static films.

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physics.flu-dyn 2026-05-11 Recognition

Large scales repeat reliably in decaying turbulence

On the repeatability of turbulence

Experiments with 30,000 repetitions find energy-carrying structures consistent across trials, unlike random small scales.

abstract click to expand

Turbulence has strong and seemingly random fluctuations. Assessing its repeatability is key to predicting flows in technology and nature, much of which decay as viscosity dissipates energy. Much has been done to this end since the work of Lorenz, but mostly in theory and simulations. Here we present experimental results from the Max Planck Variable Density Turbulence Tunnel where we generated decaying turbulence using an active grid, repeating the process with nominally identical initial conditions up to 30,000 times. In contrast with the case of stationary turbulence we found that the energy-carrying large scales show significant repeatability, irrespective of flow development time and turbulence strength. Small scales, however, can effectively be modeled by independent random variables, supporting current numerical approaches in which they are parametrised.

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physics.flu-dyn 2026-05-11 1 theorem

Localized freezing locks droplets into Cassie state

Cassie-Wenzel transition induced by localized freezing after droplet impact on supercooled micro-patterned surfaces

Tuning impact velocity and temperature on supercooled patterns stops penetration and yields non-wetting frozen shapes.

abstract click to expand

Micro-patterned surfaces have attracted significant attention in numerous applications owing to their potential to enhance hydrophobic and icephobic properties. A Cassie state of final wetting of a droplet upon impact on a micro-patterned surface, which is highly favorable for anti-icing applications, is achieved in this study through rapid localized freezing in the droplet-surface contact region via tuning the coupled interplay among droplet spreading kinetics, interfacial heat transfer, and solidification dynamics. Synchronized high-speed imaging and infrared thermography are employed to probe droplet impact and freezing dynamics, with particular emphasis on the transition of wetting state and its effect on the resulting freezing morphology. Experimental results reveal that variations in impact velocity and wall temperature lead to a final frozen wetting-state transition of the droplet from the Wenzel to the Cassie regime, accompanied by pronounced changes in freezing time, final spreading diameter, and frozen height. The transition of wetting states is attributed to rapid localized freezing at the droplet bottom, which suppresses liquid penetration into the micro-pattern. At lower impact velocities and surface temperatures, droplets tend to maintain the Cassie state with extended freezing durations, whereas higher velocities or higher temperatures promote rapid penetration and accelerated freezing. This study elucidates the coupled penetrating-freezing mechanism governed by micro-pattern design and provides fundamental insights into the rational design of anti-icing and icephobic surfaces.

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physics.flu-dyn 2026-05-11 2 theorems

Turbulence intermittency drives memoryless drop breakup

Causal mechanisms of drop breakup in turbulent flows

Outer-inner flow split shows why breakup timing ignores prior deformation and matches DNS statistics.

abstract click to expand

The fragmentation of drops and bubbles in turbulence determines the rate of many processes in engineering and environmental fluid flows. The nonlinear coupling between interfacial and hydrodynamic stresses poses a fundamental difficulty to model reduction, which we here address by decomposing the flow into outer and inner fields. We show that the outer field is independent of the drop dynamics and drives deformation, whereas the inner field responds to the deformation by dissipating the interfacial energy through the genesis of turbulent eddies. Drawing from these observations, we derive a simple analytical model that reproduces the breakup statistics obtained from ensembles of direct numerical simulations of drops and bubbles. Our results reveal a causal link between the intermittency of turbulent flows and the memoryless breakup statistics.

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physics.flu-dyn 2026-05-11 2 theorems

One PINN workflow screens turbine blade families at CFD accuracy

A fast Physics-Informed Neural Networks based approach to the 2D design of turbine blades

Progressive boundary relaxation plus dynamic loss weighting lets a mesh-free model match pressure and velocity across ten NACA6 variants and

abstract click to expand

Rapid aerodynamic screening of turbomachinery blades across wide operating envelopes remains a major computational bottleneck in preliminary design, particularly for energy-conversion and storage systems such as emerging Carnot batteries. Physics-informed neural networks (PINNs) offer a mesh-free alternative to conventional CFD, yet convergence and accuracy often deteriorate for complex blade geometries and off-design flows. We propose a progressive Euler-PINN framework that (i) gradually relaxes boundary conditions from tunnel flow without a blade to full outlet static pressure, and (ii) employs a geometry-aware dynamic loss-weighting scheme that intensifies residual penalties near highly curved boundaries. To the best of our knowledge, this is the first study to deploy a single PINN workflow for large-scale, engineering-grade screening of turbomachinery blade families across multiple operating conditions, covering ten NACA6 variants and 30 subsonic operating points. The proposed framework achieves CFD-comparable accuracy for pressure and velocity fields while reducing the computational cost required for family-wide blade screening. These results establish the method as a practical surrogate for two-dimensional turbomachinery blade pre-design and optimisation.

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physics.flu-dyn 2026-05-08

Polymers boost convective heat flux by 1100% in 2D flow

Significant heat transfer enhancement via polymer additives in two-dimensional sheared convection

Hook-like stress structures either slow the flow to mix better or form walls for strong rolls, with clear efficiency tradeoffs.

abstract click to expand

Heat dissipation is critical in modern engineering systems. Polymer additives offer a potential route to improve fluid-based cooling. Here, we study elasticity-enhanced heat transfer in two-dimensional, thermally-stratified Poiseuille flow. At Reynolds numbers, $Re$, $\lesssim 1000$, we observe two types of linearly unstable modes: the recently identified elasticity-induced centre mode (Khalid et al., J. Fluid Mech. 915, 2021) and the classical buoyancy-driven convective mode (Kelly, Adv. Appl. Mech. 31, 35-112, 1994). Direct numerical simulations show that the centre mode develops into a nonlinear `arrowhead' state but yields negligible heat transfer enhancement (typically $\approx 0.03\%$ increase compared to the conductive state). By contrast, polymers can enhance the heat flux associated with the convective mode by up to $1100\%$. The nonlinear convective-mode states take the form of either periodic orbits or travelling waves, and are dominated by hook-like polymer-stress structures that can attach to the walls. The unattached hooks act as `speed bumps' that reduced streamwise velocity and promote wall-normal motion, whereas wall-attached hooks form effective `polymer walls', reorganising the flow into strong counter-rotating rolls and triggering the extreme-enhancement regime. The elasto-buoyant nature of these states is confirmed by perturbation kinetic energy budgets, which show that polymer and buoyancy sustain the states synergistically. The wall-attached hooks enable rapid thermal equilibration but impose a large hydraulic penalty, making them suitable for process streams requiring fast temperature adjustment. Unattached hooks provide a more thermally efficient regime for heat-transport applications. These results highlight the potential of elastic fluids for future heat transfer enhancement technologies.

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physics.flu-dyn 2026-05-08 Recognition

AI agent discovers turbulence correction cutting CFD error 7.89%

AI CFD Scientist: Toward Open-Ended Computational Fluid Dynamics Discovery with Physics-Aware AI Agents

Vision checks on flow images let the system validate code changes and produce credible results on a periodic hill benchmark.

abstract click to expand

Recent LLM-based agents have closed substantial portions of the scientific discovery loop in software-only machine-learning research, in chemistry, and in biology. Extending the same loop to high-fidelity physical simulators is harder, because solver completion does not imply physical validity and many failure modes appear only in field-level imagery rather than in solver logs. We present AI CFD Scientist, an open-source AI scientist for computational fluid dynamics (CFD) that, to our knowledge, is the first to span literature-grounded ideation, validated execution, vision-based physics verification, source-code modification, and figure-grounded writing within a single inspectable workflow. Three coupled pathways cover parameter sweeps within a fixed solver, case-local C++ library compilation for new physical models, and open-ended hypothesis search against a reference comparator, all running on OpenFOAM through Foam-Agent. At the center of the framework is a vision-language physics-verification gate that inspects rendered flow fields before any result is accepted, rerun, or written into a manuscript. On five tasks under a shared GPT-5.5 backbone, AI CFD Scientist autonomously discovers a Spalart-Allmaras runtime correction that reduces lower-wall Cf RMSE against DNS by 7.89% on the periodic hill at Reh=5600; under matched LLM cost, two strong general AI-scientist baselines (ARIS, DeepScientist) execute partial CFD workflows but lack the domain-specific validity gates needed to convert runs into defensible scientific claims; and a controlled planted-failure ablation shows that the vision-language gate detects 14 of 16 silent failures missed by solver-level checks. Code, prompts, and run artifacts are released at https://github.com/csml-rpi/cfd-scientist.

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physics.flu-dyn 2026-05-08

AI agent finds turbulence fix that cuts wall shear error 7.89 percent

AI CFD Scientist: Toward Open-Ended Computational Fluid Dynamics Discovery with Physics-Aware AI Agents

The system checks images of flow fields to validate a runtime change to the Spalart-Allmaras model on periodic hill flow at Re 5600.

abstract click to expand

Recent LLM-based agents have closed substantial portions of the scientific discovery loop in software-only machine-learning research, in chemistry, and in biology. Extending the same loop to high-fidelity physical simulators is harder, because solver completion does not imply physical validity and many failure modes appear only in field-level imagery rather than in solver logs. We present AI CFD Scientist, an open-source AI scientist for computational fluid dynamics (CFD) that, to our knowledge, is the first to span literature-grounded ideation, validated execution, vision-based physics verification, source-code modification, and figure-grounded writing within a single inspectable workflow. Three coupled pathways cover parameter sweeps within a fixed solver, case-local C++ library compilation for new physical models, and open-ended hypothesis search against a reference comparator, all running on OpenFOAM through Foam-Agent. At the center of the framework is a vision-language physics-verification gate that inspects rendered flow fields before any result is accepted, rerun, or written into a manuscript. On five tasks under a shared GPT-5.5 backbone, AI CFD Scientist autonomously discovers a Spalart-Allmaras runtime correction that reduces lower-wall Cf RMSE against DNS by 7.89% on the periodic hill at Reh=5600; under matched LLM cost, two strong general AI-scientist baselines (ARIS, DeepScientist) execute partial CFD workflows but lack the domain-specific validity gates needed to convert runs into defensible scientific claims; and a controlled planted-failure ablation shows that the vision-language gate detects 14 of 16 silent failures missed by solver-level checks. Code, prompts, and run artifacts are released at https://github.com/csml-rpi/cfd-scientist.

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physics.flu-dyn 2026-05-08

Tensor model reconstructs visco-plastic flows without integration

Reduced-Order Modeling of Parameterized Visco-Plastic Shallow Flows

Low-rank decomposition of snapshot data over parameter grids yields fast surrogates that track fronts and yield surfaces in Herschel-Bulkley

abstract click to expand

We propose a non-intrusive reduced-order modeling framework for parametrized visco-plastic free-surface flows governed by a shallow-water formulation of Herschel--Bulkley fluids. These flows exhibit strong nonlinearities, non-smooth rheology, moving fronts, and yield surfaces, making efficient surrogate modeling particularly challenging. To address this challenge, we employ a tensor-based approach in which the solution manifold is approximated using a low-rank representation obtained via higher-order singular value decomposition of snapshot data over a structured parameter space. The resulting tensorial reduced-order model (TROM) enables rapid online evaluation by directly reconstructing solution trajectories from the compressed representation, thereby avoiding the need to perform time integration of a reduced dynamical system. The proposed non-intrusive framework can be interpreted as an encoder--decoder architecture with a compressed latent representation and efficient multilinear decoding. Numerical experiments demonstrate that the proposed approach accurately captures key flow features, including front propagation, plug and shear regions, and near-stopping dynamics, while achieving substantial computational speedups relative to full-order simulations.

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physics.flu-dyn 2026-05-08

Exponential scaling collapses mixing times across density differences

Mixing of miscible liquids: Dimensionless scaling for intermediate-to-large density differences in a stirred tank

Power, Froude and Richardson numbers bring all dimensionless mixing data onto one master curve in stirred tanks

abstract click to expand

Mixing of miscible liquids is an essential process in multiple industrial settings, usually with the intent to homogenize the product. This seemingly simple process is in fact a complex hydrodynamic problem that has a direct impact on the product quality. In this study, numerical simulations of a stirred tank were performed with a 50/50 ratio of liquids and systematically varied the Reynolds and Richardson numbers. A positive correlation between the mixing time and the Richardson number was observed, as reported in the literature. The influence of the Reynolds number was not as pronounced and clear. Based on the Power, Froude and Richardson numbers, we were able to derive an exponential scaling for the dimensionless mixing time that collapsed all our data onto one master curve.

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physics.flu-dyn 2026-05-08

Optimized designs lift heat exchanger performance by 22 percent

Topology optimization of two-fluid turbulent heat exchangers: A Darcy flow-based multifidelity approach

Calibrated low-fidelity Darcy model lets topology search find turbulent two-fluid exchangers with better heat transfer and controlled drag

abstract click to expand

This paper presents a topology optimization method for designing two-fluid heat exchangers under turbulent conditions using a Darcy flow-based low-fidelity (LF) model. The LF model is calibrated against a high-fidelity (HF) model based on the Reynolds-averaged Navier-Stokes (RANS) equations to increase the accuracy of predictions for fluid flow and heat transfer characteristics. Since the discrepancies between the LF and HF models can be significant, particularly for pressure drops, a multifidelity topology optimization framework is adopted to leverage the strengths of both models. Using the calibrated LF model, we perform topology optimization for various inlet velocities in the boundary conditions and trade-off parameters in the objective function to obtain diverse optimized designs. The optimized designs are then evaluated using the HF model to assess their performance with higher accuracy. The results demonstrate that the optimized designs significantly improve overall heat transfer coefficients while maintaining manageable pressure drops, achieving up to a 22% higher performance evaluation criterion (PEC) compared to a reference design enhanced by conventional twisted tape insertion. The improvements are attributed to the optimized configurations that promote enhanced fluid mixing and increased surface area for heat exchange, yet maintain streamlined flow paths to minimize pressure losses. Overall, the proposed topology optimization method using the Darcy flow-based LF model proves effective in designing high-performance double pipe heat exchangers, showcasing the potential of the multifidelity approach in overcoming the challenges of optimizing heat exchangers under turbulent flow conditions.

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physics.flu-dyn 2026-05-08

Mist cooling best balances protection and performance in ODE combustors

Comparative Numerical Study of Film Cooling Strategies for Thermal Protection of a Kerosene-Fueled Oblique Detonation Combustor

Simulations at Mach 10 show liquid kerosene mist reduces wall heat with minimal wave disruption at low coolant levels.

abstract click to expand

Thermal protection remains a critical challenge for oblique detonation engines (ODEs) operating under hypersonic conditions due to the extreme heat release and compact combustor geometry associated with oblique detonation waves (ODWs). In the present study, the effectiveness of film cooling for a kerosene-air ODE combustor is numerically investigated under a flight Mach number of 10 and an altitude of 15 km. Three active cooling strategies are considered, including air film cooling, gaseous-kerosene film cooling, and liquid-kerosene mist cooling. The results show that all cooling strategies preserve stable oblique-detonation propagation and maintain the canonical wave-system structure within the investigated operating range. Air cooling produces stronger disturbances near the initiation region and triple point, resulting in enhanced downstream wave interactions and larger propulsion penalties. In contrast, fuel-based cooling induces milder disturbances and better preserves the global detonation structure. All cooling methods substantially reduce the near-wall thermal load, although their cooling characteristics differ significantly. Gaseous-kerosene film cooling exhibits a spatially periodic near-wall thermal response associated with the discrete cooling hole arrangement, while liquid-kerosene mist cooling produces a smoother near-wall temperature distribution due to enhanced two-phase mixing and phase-change heat absorption. Among the investigated strategies, mist cooling provides the best overall balance between thermal protection and propulsion performance at coolant mass ratios of 1%-3%, whereas gaseous-kerosene film cooling becomes advantageous at higher injection levels due to improved wall coverage continuity. The present results demonstrate the feasibility and potential of fuel-based film cooling for thermal management in hypersonic ODE combustors.

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physics.flu-dyn 2026-05-08

Three-phase model captures hydraulic jumps over wide Froude range

Numerical Modeling of Flow and Air Entrainment in Hydraulic Jumps for a Wide Range of Froude Numbers

Matches experiments from seven labs at 300-fold lower cost than IDDES while using 400 times fewer grid cells.

abstract click to expand

The numerical modeling of hydraulic jumps remains challenging due to complex interactions among free-surface deformation, air entrainment and detrainment, and turbulent bubble transport. Whereas accurate prediction of these flows is essential for the design of hydraulic structures, existing high-fidelity tools require prohibitive computational resources for engineering applications. This study implements a three-phase mixture model based on an Unsteady Reynolds-Averaged Navier Stokes (URANS) framework, to numerically simulate flow and air entrainment across twelve hydraulic jumps with Froude numbers ranging from $1.98$ to $8.48$, representing the first systematic analysis for such a comprehensive range of Froude numbers. The model accurately represents time-averaged velocity fields and air concentration profiles, as well as dynamic features including jump toe oscillation and free-surface deformation, showing good agreement with experimental data from seven facilities. Compared to Improved Delayed Detached Eddy Simulations (IDDES), the proposed approach achieves similar accuracy with approximately 400-fold fewer cells and a 300-fold reduction in computational cost. The investigation shows that the selection of turbulence closure affects the accuracy of the prediction of air entrainment. These findings establish the three-phase mixture approach as a practical engineering tool for hydraulic jump simulation, offering an effective balance of accuracy and computational cost.

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physics.flu-dyn 2026-05-08

Rapidly rotating convection reaches ultimate heat transport scaling

Rigorous ultimate scaling in rapidly rotating steady convection

Single-mode columnar solutions attain diffusivity-free Nusselt and Reynolds numbers with logarithmic boosts for specific wavenumbers.

abstract click to expand

Rapidly rotating Rayleigh-B\'enard convection admits a class of exact steady single-mode solutions describing high-amplitude convection cells. Using a matched asymptotic analysis in the high-Rayleigh-number limit, we obtain a rigorous characterization of their bulk and boundary-layer structure, yielding explicit scaling laws for the Nusselt and Reynolds numbers, including their dependence on the horizontal wavenumber. We show that, for suitable wavenumbers, these solutions attain the diffusivity-free ultimate scalings frequently assumed for geophysical and astrophysical convection, with additional enhancing logarithmic corrections. This reveals a specific mechanism through which rapidly rotating convection can approach ultimate heat transport via coherent columnar structures with well-defined horizontal scales.

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physics.flu-dyn 2026-05-07

Rough ice focuses droplet hits to build taller bumps

LES of Droplet Impingement: Application to Clean and Laser-Scanned Ice Shapes

LES of laser-scanned shapes shows upstream-face impingement creates a self-reinforcing loop that amplifies roughness during icing.

abstract click to expand

The prediction of aircraft icing is conventionally performed using multishot simulation frameworks that fail to predict the progressive roughening of the ice surface. To understand roughness formation, we investigate droplet impingement on clean and laser-scanned rough ice shapes using a high-fidelity computational framework based on wall-modeled large-eddy simulations and Lagrangian particle tracking. This methodology is validated against experimental data for a NACA 23012 airfoil and a NACA 64A008 swept tail, accurately predicting collection efficiency and supercooled large droplet splashing. The framework is subsequently applied to laser-scanned rime ice geometries to quantify the impact of surface roughness on local impingement distributions. The results reveal that physical roughness induces a highly nonuniform collection efficiency, with droplet impingement intensely concentrated on upstream-faces of roughness elements, creating sheltered shadow zones immediately downstream. While the spanwise-averaged collection efficiency remains remarkably similar to that of an equivalent smooth body, idealized smooth surfaces completely suppress these localized impingement peaks. Ice accretion simulations demonstrate that this localized impingement creates a self-reinforcing feedback loop, actively amplifying existing roughness features over time. These findings provide a direct physical explanation for the formation of characteristic rime ice structures and highlight the critical role of local surface topology in the accretion process.

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physics.flu-dyn 2026-05-07

Adjoint gradients cut airfoil drag 22% under buffet limit

Buffet Alleviation via Linear Stability Adjoint

Linear stability eigenvalue sensitivities replace empirical rules for transonic shock oscillation constraints in shape design.

abstract click to expand

Transonic buffet, self--sustained shock and shear--layer oscillations, imposes hard limits on the cruise envelope of modern transport aircraft, and avoiding it is a primary design driver. State-of-the-art buffet-onset criteria used in design, such as the $\Delta\alpha = 0.1^\circ$ criterion and separation--sensor methods, are empirical surrogates rather than first--principle predictors, and can yield either overly conservative or unsafe designs. Linear stability analysis (LST) predicts buffet onset directly from the spectrum of the linearized operator about the steady base flow, but using it as an aerodynamic shape optimization constraint has been bottlenecked by the cost of differentiating an eigenvalue with respect to many design variables. In this paper, we develop a coupled adjoint method that efficiently computes the sensitivity of the dominant LST eigenvalue with respect to a large number of shape design variables, by reusing the steady CFD adjoint within a top and bottom level decomposition of the eigenproblem. We verify the eigensolver and adjoint against the canonical cylinder vortex--shedding benchmark, then verify the LST predictions on the OAT15A supercritical airfoil at $M=0.73$, $Re=3.2\times 10^{6}$ against published eigenspectra and against the linear growth phase of a URANS run. Using the resulting gradients, a single-point buffet-constrained drag minimization of the OAT15A achieves a $22.4\%$ drag reduction while satisfying the LST-based buffet constraint. Finally, we present preliminary three-dimensional results on the wing only NASA common research model (CRM) at $M=0.85$, $Re=5\times 10^{6}$, recovering buffet onset at $\alpha \approx 4.0^\circ$ from a sweep of warm--started URANS runs and providing a stepping stone toward three-dimensional buffet-constrained wing optimization with the present adjoint.

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physics.flu-dyn 2026-05-07

Ground blocks downward wake expansion

Modelling Farm-to-Farm Interaction Using a Fast Linearised Numerical Approach

Linearised model finds this makes downstream farms with taller turbines lose more power to upstream wakes than shorter ones do.

abstract click to expand

This paper presents a computationally efficient, linearised numerical method for modelling aerodynamic interactions between wind farms. The linearised two-dimensional incompressible equations are solved using Fourier transforms in the horizontal direction and finite-difference discretisation in the vertical. Model predictions are validated against large-eddy simulation (LES) data, focusing on a tandem wind farm configuration where a downstream wind farm operates within the wake of an upstream array. A parametric study is then conducted to examine the impact of this wake on the performance of the downstream farm across a range of inter-farm distances and hub-height ratios. We demonstrate that the upward vertical displacement of these wakes is driven by asymmetric turbulent entrainment caused by the farm's proximity to the ground, which restricts downward wake expansion. Consequently, the results suggest that, due to this upward wake displacement, downstream wind farms with higher hub heights may be more strongly affected by upstream farms than those with lower hub heights.

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physics.flu-dyn 2026-05-06 3 theorems

Latent-space model turns coarse event images into high-res flow fields

Real-Time Estimation of High-Resolution Flow Fields and Reduced-Order Coordinates from Event-Based Imaging Velocimetry

Offline POD training plus online Kalman estimation recovers consistent turbulence statistics from deliberately low-resolution real-time data

abstract click to expand

We propose a data-driven framework to estimate high-resolution (HR) velocity fields and reduced-order flow coordinates from real-time Event-Based Imaging Velocimetry (rt-EBIV). Fast event analysis first provides low-resolution (LR) velocity snapshots on a coarse grid. Offline, paired LR/HR fields are used to identify the LR-to-HR mapping and a linear dynamical model in a POD-based latent space. Online, each LR snapshot is projected onto the LR basis, the corresponding HR coordinates are estimated and temporally regularized, and the HR field is reconstructed from the retained POD modes. Three estimators are compared: a direct Kalman filter (KF), a linear stochastic estimator followed by Kalman filtering (LSE), and a variance-rescaled variant (LSE+VR). The method is tested on two turbulent flows acquired with pulsed EBIV: a submerged water jet and a channel flow over a square rib. All estimators outperform direct cubic interpolation of the LR fields, yielding more consistent HR reconstructions of instantaneous flow states, turbulent kinetic energy, spectra, reduced-order dynamics, and temporal coherence. LSE gives the lowest overall reconstruction error, while LSE+VR achieves similar errors with improved recovery of fluctuation energy and higher-order content. The direct KF is the most computationally efficient and provides the closest agreement with the HR reference in spectral analyses. Since most of the cost is associated with full-field HR reconstruction, the latent-coordinate estimation is negligible compared with LR processing. The framework allows deliberately coarse rt-EBIV processing to be combined with reduced-order refinement, extending real-time operation toward higher update rates while preserving richer and dynamically consistent HR flow representations for diagnostics and future observer-based flow-control applications.

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physics.flu-dyn 2026-05-06

Balance of horizontal and vertical flows maximizes heat transfer

Geometry-controlled heat transport pathways and optimal heat transfer in differentially heated cavities

Simulations across three decades of cavity shapes identify four regimes and show the peak occurs at velocity ratio 0.45 independent of how強く

abstract click to expand

We perform direct numerical simulations of natural convection in a differentially heated cavity over Rayleigh number $Ra=10^6$--$10^8$ at Prandtl number $Pr=0.7$, systematically varying the aspect ratio over $0.1 \leq \Gamma \leq 60$. Across this nearly three-decade range, the Nusselt number $Nu$ exhibits four distinct power-law regimes as a function of $\Gamma$, arising solely from geometric confinement. We show that these transport regimes are governed by qualitative changes in the anisotropy and structure of the large-scale circulation (LSC), quantified by the ratio of Reynolds numbers based on the root-mean-square horizontal and vertical velocities, $Re_u/Re_v$. For small $\Gamma$, vertical confinement promotes a horizontally dominant LSC and strong enhancement of heat transport. At intermediate aspect ratios, the circulation reorganizes into an efficient heat-carrying structure for which $Nu$ becomes nearly independent of $\Gamma$. At larger $\Gamma$, the LSC becomes increasingly vertically elongated and transitions to shear-driven dynamics associated with Kelvin--Helmholtz-type instability, leading to a progressive reduction in heat transport before approaching an asymptotic large-$\Gamma$ limit. A central result is that the heat flux is maximized when the circulation anisotropy satisfies $Re_u/Re_v \approx 0.45$, which remains robust across all Rayleigh numbers considered. The corresponding optimal aspect ratio follows the scaling $\Gamma_{\mathrm{opt}} \sim Ra^{-0.19}$. Resolvent analysis further reveals that optimal transport is associated with stationary, slender response modes, whereas larger $\Gamma$ results in oscillatory shear-layer amplification. These findings establish geometric confinement as the key control parameter governing transport pathways in differentially heated cavities and provide a predictive framework for geometry-driven heat-transfer optimization.

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physics.flu-dyn 2026-05-06

Hurricane boundary layers scale by vorticity and friction velocity

Turbulent Boundary Layer Height Scales in Hurricanes

Formulas using u_star/beta and u_star/sqrt(beta N) predict heights to 2.5% error and collapse observed wind profiles.

abstract click to expand

Boundary layer processes drive the air-sea exchange of momentum, heat, and moisture that powers and shapes hurricanes. The height of the boundary layer is a critical parameter in engineering and meteorological models of hurricane wind speed, turbulence intensity, and storm strength. Existing models rely on a height scale derived with the assumption of a constant eddy viscosity, a strong simplification that limits physical accuracy. This work proposes formulae for the turbulent boundary layer height in hurricanes outside the eyewall. The proposed scalings are $u_\star/\beta$ for neutral stratification, and $u_\star/\sqrt{\beta N}$ for stable stratification, where $u_\star$ is the friction velocity, $\beta$ is the absolute fluid vorticity and N is the Brunt-Vaisala frequency of the background stratification. These scalings are analogous to those used in the literature for neutrally and stably stratified turbulent atmospheric boundary layers. The formulae are backed by analytical derivation and validated against velocity profiles from large-eddy simulations and field observations. They are predictive to within 2.5% relative error on average and yield a good collapse of the simulated and observational velocity profiles away from the surface. The results further enable quantitative relationships between boundary layer height and other characteristic scales, including the height of maximum wind speed and the depth of the inflow layer. The proposed expressions offer a practical basis for interpreting observational data, informing mesoscale simulations, and specifying turbulent flow statistics in wind engineering and coastal resilience.

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physics.flu-dyn 2026-05-06

Barotropic reentrant channel models with topography show that low bottom drag allows…

A frictional control mechanism of circumpolar transport in barotropic reentrant channel models

In low-drag barotropic channel models, Rossby waves from barotropic instability transport westward momentum to form and sustain a westward…

abstract click to expand

Recent studies have reported that an increase in the bottom drag coefficient can enhance the volume transport of the Antarctic Circumpolar Current. Several mechanisms have been proposed to explain this frictional control, including the regulation of the geostrophic velocity by baroclinic instability and the influence of the form stress associated with standing meanders and wind-driven gyres. In this study, the role of momentum transport associated with Rossby wave radiations from disturbances is investigated as a potential frictional control mechanism. To highlight roles of the Rossby wave radiation, numerical experiments are conducted using barotropic reentrant channel models with topographic obstacles. In the high-drag regime, the circumpolar component is wind-driven, and the imbalance between the westerlies and topographic form stress sustains a net eastward transport. In contrast, in the low-drag regime, the eddy-driven westward circumpolar current is formed. In this case, the eastward flow at the center of the double gyre becomes unstable to barotropic instability. Analyses of the wave activity flux and momentum budget indicate that the Rossby wave transports westward momentum both northward and southward from the unstable region, which is responsible for the westward circumpolar current formation and maintenance. Although the direct application of the barotropic channel model to oceans requires caution, our findings imply that Rossby wave radiations from jets may play a role in the frictional control of the Antarctic Circumpolar Current.

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physics.flu-dyn 2026-05-06

Deeper submergence boosts robot swimming speed by over 10%

Tethering and depth of submergence affect the swimming performance of undulatory robots

Tethered tests link the gain to lower wave drag away from the surface and show tethering cuts roll costs at the surface.

abstract click to expand

Over the past few decades, biomimetic robotic experiments have significantly advanced our understanding of undulatory swimming. Compared to animal experiments, robotic experiments offer repeatability and controlled parameter variations, but the robots operate under constraints that differ from those experienced by their natural counterparts. Freely swimming robots often remain on the surface, whereas most undulatory fish, including eels, are typically fully submerged during locomotion. Studies focusing on submerged swimming commonly rely on tethered robots to maintain depth control. This study examines the performance implications of surface versus submerged swimming, and tethered versus free swimming, using the robotic undulatory swimmer 1-guilla. The robot was tested in two configurations: free swimming in a pool and tethered swimming in a water channel at the surface and at varying depths down to three body heights. We varied kinematic input parameters and quantified performance in terms of swimming speed, cost of transport, and body kinematics. Our results reveal that at the surface, tethered swimming achieves speeds comparable to free swimming but at a lower energetic cost. This reduction in cost of transport is attributed to the suppression of body roll during tethered operation. Increasing submergence depth improved both the maximum speed and energy efficiency by more than 10% relative to the surface swimming performance. As the body kinematics remained unchanged when submerged, the performance deficit near the surface is attributed to increased wave drag. Overall, our findings provide explanations and insights into discrepancies in results obtained for tethered and free-swimming robotic studies, they highlight the hydrodynamic challenges of surface locomotion, and can help explain why natural undulatory swimmers predominantly favor submerged propulsion.

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physics.flu-dyn 2026-05-06

Stratification halts vertical scalar mixing after early growth

Evolution of passive scalar mixing layers in stratified and unstratified homogeneous turbulence

The vertical layer stops spreading once its width matches the vertical integral length of horizontal velocity, keeping the Froude number of

abstract click to expand

High-resolution large-eddy simulations of decaying stratified and unstratified homogeneous turbulence are used to understand the mixing of passive scalars in stably stratified flows. Two passive scalar mixing layers, one in the vertical direction and the other in the transverse direction, are a model for a plume that is very large relative to the length scale of the velocity. In the transverse direction, the evolution of the passive scalar is broadly similar in the stratified and unstratified cases, although it does spread slightly faster when stratified. Also, the intensity of the scalar fluctuations is higher in the stratified case, and the turbulent/non-turbulent interface is more intermittent. In the vertical direction, though, the stratified case has almost no mixing because the stratification prevents large-scale stirring. Initially, the stratified passive layer grows until its width is proportional to the vertical integral length of the horizontal velocity, which is itself constrained to maintain the vertical Froude number order one. After this early growth, there is little additional spreading of the passive scalar. Modelling of the stratified scalar flux in the transverse direction is done effectively with a one-constant model if the mean profile is known, and a two-constant model if the profile shape must be assumed. In the latter case, the model is good only if the scalar is in quasi-equilibrium with the velocity field such that the length scale of the scalar can be scaled from the kinetic energy. In this study, the Prandtl number of the active and passive scalars is 0.7. It is anticipated that the reverse buoyancy flux resulting from higher Prandtl numbers will affect the passive scalar mixing.

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physics.flu-dyn 2026-05-06

Inertial particles gather where turbulence weakens

Turbophoresis of inertial particles in inhomogeneous turbulence produced by oscillating grids

Grid experiments isolate turbophoresis and show particles concentrate in lower-intensity zones after tracer normalization.

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Formation of large-scale inhomogeneous distributions of inertial solid particles in a small-scale inhomogeneous turbulence is caused by a phenomenon of turbophoresis. This effect is described in terms of an effective turbophoretic velocity that is proportional to the product of the particle Stokes time and the gradient of turbulence intensity and is directed to the minimum turbulent velocity. We study turbophoresis of inertial particles in experiments with an inhomogeneous turbulence produced by one and two oscillating grids in the airflow. Particle Image Velocimetry is used to measure the fluid velocity and the spatial distributions of inertial particles. To isolate the effect of turbophoresis, the number density for inertial particles in every point is normalized by that for noninertial particles obtained in the separate experiments for the same flow conditions. The experiments demonstrate that inertial particles are accumulated within the large-scale concentrations located in the regions with a lower turbulence intensity in agreement with theoretical predictions.

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physics.flu-dyn 2026-05-06 3 theorems

Inertial particles cluster where turbulence is weakest

Turbophoresis of inertial particles in inhomogeneous turbulence produced by oscillating grids

Oscillating-grid experiments confirm accumulation in low-intensity zones after isolating the turbophoretic effect.

abstract click to expand

Formation of large-scale inhomogeneous distributions of inertial solid particles in a small-scale inhomogeneous turbulence is caused by a phenomenon of turbophoresis. This effect is described in terms of an effective turbophoretic velocity that is proportional to the product of the particle Stokes time and the gradient of turbulence intensity and is directed to the minimum turbulent velocity. We study turbophoresis of inertial particles in experiments with an inhomogeneous turbulence produced by one and two oscillating grids in the airflow. Particle Image Velocimetry is used to measure the fluid velocity and the spatial distributions of inertial particles. To isolate the effect of turbophoresis, the number density for inertial particles in every point is normalized by that for noninertial particles obtained in the separate experiments for the same flow conditions. The experiments demonstrate that inertial particles are accumulated within the large-scale concentrations located in the regions with a lower turbulence intensity in agreement with theoretical predictions.

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physics.flu-dyn 2026-05-06

Scheme conserves total energy and enforces pressure equilibrium for real gases

Pressure-equilibrium-preserving and fully conservative discretization of compressible flow equations for real and thermally perfect gases

Nonlinear fluxes depending on any equation of state avoid oscillations and conservation trade-offs in supercritical and transcritical flows.

abstract click to expand

Numerical simulations of compressible real-fluid flows are notoriously plagued by spurious pressure oscillations arising in regions of abrupt flow variations. As a possible remedy, several numerical formulations enforce the pressure equilibrium condition for the compressible Euler equations, typically at the cost of spoiling the correct conservation of total energy or by overspecifying the thermodynamical variables. This study proposes for the first time a numerical discretization procedure which is able to discretely preserve the full conservation of the linear invariants (mass, momentum and total energy) and to exactly enforce the pressure equilibrium condition. The method also preserves the conservation of kinetic energy by convection, and is based on the specification of nonlinear numerical fluxes for mass and internal energy which depend on the details of the equation of state. Both thermally perfect and real gases with an arbitrary equation of state are considered, and a simplified approximate pressure equilibrium preserving formulation with excellent performances is also proposed. The effectiveness of the novel formulations is assessed through a series of numerical simulations in supercritical and transcritical conditions with some of the most popular cubic equations of state.

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physics.flu-dyn 2026-05-06

Soluble surfactants hold surface tension steady until pinch-off

Interface pinch-off in the presence of a soluble surfactant

Millimeter droplets with Surfynol 465 or SDS match diffusion model to 20 microseconds before breakup

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We study numerically and experimentally the breakup of a pendant droplet loaded with a soluble surfactant. We consider the limit in which surfactant sorption is limited only by diffusion. Surfactant transfer toward the interface is enhanced by convection. As a consequence, diffusion does not constitute a significant barrier over most of the breakup, and surfactant sorption maintains the surface tension practically constant across the interface. Diffusion hinders the surfactant sorption only very close to the interface pinch-off. The droplet shape in the diffusion-limited model deviates significantly from that in the insoluble case over most of the breakup. In the insoluble case, the droplet shape is affected by surfactant depletion, which leads to a local increase in surface tension and Marangoni stress. The dynamics of a millimeter-sized droplet loaded with Surfynol 465 agree remarkably well with predictions from the diffusion-limited model, without any parameter fitting, down to pinching times of the order of $10-20$ $\mu$s. Sodium dodecyl sulfate (SDS) produces essentially the same effects as those for Surfynol 465. Therefore, both Surfynol 465 and SDS maintain a practically constant surface tension throughout most of the droplet breakup. Slow-kinetics surfactants, such as Triton X-100, differ significantly from Surfynol 465 and SDS. The most evident effect of the surfactant adsorption energy barrier is the shortening of the filament that bridges the upper meniscus and the detached lower drop. Comparing the filament length to that of a clean interface with the same surface tension allows one to evaluate the rate of surfactant adsorption.

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physics.flu-dyn 2026-05-06

Harmonic balance speeds periodic gas flows up to 9 times

A Time-Domain Harmonic Balance Unified Gas-Kinetic Scheme for Temporally Periodic Flows Across all Knudsen Regimes

Reformulating the repeating problem as coupled harmonics lets pseudo-time marching replace repeated full cycles while keeping accuracy from

abstract click to expand

This paper introduces a time-domain harmonic balance unified gas-kinetic scheme (HB-UGKS) designed to simulate temporally periodic flows across all Knudsen regimes. The harmonic balance approach reformulates the periodic problem into a block-coupled, quasi-steady system via a time-spectral source term. This allows for pseudo-time marching, local time-stepping, and the concurrent resolution of all sub-time levels, drastically reducing wall-clock time. Coupled with the UGKS-which maintains essential transport-collision coupling in its flux evaluations--the framework ensures multiscale validity across the entire Knudsen number range. The method is validated against two representative cavity flows. For a shear-driven oscillatory cavity under small-amplitude excitation, the fundamental harmonic alone accurately resolves the flow dynamics across various Knudsen and Strouhal numbers, successfully capturing the anti-resonance phenomenon and matching hydrodynamic damping predictions from linearized Boltzmann analyses. For a thermally driven cavity with large temperature modulations, higher-order harmonics prove essential to capture strong nonlinear waveform distortions and rarefaction effects. Beyond its physical fidelity, the HB-UGKS demonstrates substantial computational efficiency over explicit time-domain methods. This advantage peaks in high-frequency regimes, achieving speedup factors of 9.0 and 8.26 for the shear-driven and thermally driven cases, respectively.

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physics.flu-dyn 2026-05-06

Phase alignment triggers instability in oscillating shear

Flow instability in Stokes layer of Carreau fluids

Carreau-fluid analysis shows disturbances grow only when their velocity stays synchronized with the time-varying base flow.

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This study investigates the influence of shear-thinning on the instability of a prototype time-periodic flow, the Stokes layer, in Carreau fluids. The time-dependent base flow was solved using a numerical method and a binomial expansion method. The expansion is conducted in terms of the nondimensional characteristic time ($\Lambda$), which quantifies the fluid's response time in viscosity to changes in shear rate. The expansion method shows good agreement with the numerical solution, provided that $\Lambda$ remains small. To understand the effect of shear-thinning on time-periodic flow instability, a Floquet analysis was conducted to examine two key parameters of the Carreau model, i.e., $\Lambda$ and the power-law exponent $n$. Our results show that decreasing $n$, which signifies stronger shear-thinning behavior, has a monotonic stabilizing effect on the flow within the range of investigated $n$. In contrast, increasing $\Lambda$ has a non-monotonic effect on the flow instability, which can be observed in both the weakly and strongly shear-thinning regimes. To clarify the instability mechanism, we perform an energy analysis showing that instability arises when the perturbation field is in phase with the oscillatory base flow, enabling efficient energy extraction from the time-dependent shear. A phase mismatch suppresses this transfer and stabilises the flow. This mechanism parallels the classical energy-production process in steady shear flows, where streamwise and wall-normal velocity perturbations exhibit a characteristic phase difference. Crucially, it is identified here for the first time in a time-periodic shear flow.

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physics.flu-dyn 2026-05-06

Squid soft nozzles boost jet impulse over 300% via timed recoil

Squid-inspired soft superpropulsion

A compliant funnel stores energy during mantle contraction and returns it during expulsion when its response time matches jet acceleration.

abstract click to expand

Squid span four orders of magnitude in size yet rely on pulsed jets. We show that the funnel (siphon) is a compliant nozzle whose dilation and recoil lag mantle contraction, storing and returning energy within each pulse, a mechanism we term superpropulsion. Histology reveals a collagen sheath, and chromatophore tracking in two squid species quantifies a repeatable phase lag. Engineered nozzles, 3D fluid-structure simulations, and a reduced-order mathematical model predict > 300% impulse amplification when nozzle response time matches jet acceleration (tau/T = 0.2-0.4), overlapping in vivo timing. Tuned nozzles extend jet reach, enhance plume dispersion, and improve jet-driven boat transport, with gains persisting after 40x miniaturization. Superpropulsion recasts pulsed jets as impedance matching, with a soft nozzle acting as an elastic capacitor that passively shapes impulse delivery in soft robotic thrusters and fluidic actuators.

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physics.flu-dyn 2026-05-05

Triad phases set cascade direction in 2D turbulence

Triad phase dynamics determine cascade direction in two-dimensional turbulence

A stochastic model of phase sums in Fourier triads predicts forward or inverse energy transfer from the spectrum alone and with no free参数.

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Despite their importance in turbulence theory, a unifying and predictive rule determining the direction of the cascades of conserved quantities is lacking. In this work, we show that the direction of the cascades in two-dimensional turbulence is encoded in the complex phases of the Fourier transform of the velocity field. We develop a closure for the dynamics of a triad phase, the sum of the phases of three modes forming a triad, based on the observation that neighboring triad phases are weakly correlated. The resulting stochastic model can be solved analytically to find the triad phase probability distribution function (PDF). We validate our model's assumptions and predictions using an ensemble of two-dimensional turbulence simulations. From the triad phase PDF we develop a novel closure of the energy equation, and prove that the cascade directions are determined by our model without adjustable parameters and given only the energy spectrum. Triad phase dynamics occur in any quadratically nonlinear partial differential equation, making this a promising new direction in the study of strongly out-of-equilibrium systems.

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physics.flu-dyn 2026-05-05 2 theorems

Lattice Boltzmann matches literature for unconfined cylinder flow

Lattice Boltzmann methodology for unconfined flows

Domain of 10D upstream, 30D downstream, 10D wide with special boundaries gives accurate drag and lift at Re 100.

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Numerical analysis of unconfined flow over an obstacle has always been challenging in computational fluid dynamics due to the truncation of the computational domain while replicating the real-life flows and the application of the boundary conditions. Confined flows studies have been well established and documented while unconfined flow studies are relatively challenging. Present work demonstrates the implementation of lattice Boltzmann method for unconfined flow over a circular cylinder for Re 100. The cylinder was placed at 10D upstream and 30D downstream and 10D from both the top and bottom walls. Different boundary conditions were implemented at the top and bottom walls to ensure unconfined flow. Drag and lift coefficients are also presented and were computed using the momentum exchange algorithm. Results are in complete agreement with the existing literature which demonstrate the capability of the solver.

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physics.flu-dyn 2026-05-04

Turbulence scaling exponents level off at 2.2 for high orders

Experimental Evidence for Longitudinal Scaling Exponent Saturation in Shear Turbulence

Experiments in shear layers at Re_lambda 1400 find moments of velocity differences saturate, consistent with vortex filament dominance.

abstract click to expand

The asymptotic behavior of velocity statistics in the tails of distributions and at high Reynolds numbers remains unresolved in turbulence. To investigate this behavior we measured the $n$th-order moments of the distributions of longitudinal velocity differences, $S_n(r) \equiv \langle [u(x+r)-u(x)]^n \rangle \sim r^{\zeta_n}$, in turbulent shear layers at Taylor-scale Reynolds numbers up to $Re_\lambda \approx 1400$. We used a nanoscale hot-wire probe with a sensing length, $l_w$, that was about half the Kolmogorov scale, $\eta$. We obtained datasets that were up to $5\times 10^7$ integral timescales long, so that the statistics converged up to $n=14$. In the inertial range, the exponents, $\zeta_n$, deviate from classical models and appear to saturate near $\zeta_n \approx 2.2 \pm 0.1$ for $n \gtrsim 12$. The saturation in the exponents is supported by a collapse of the tails of the velocity-difference distributions, and by plateaus in their compensated moments. These results constitute the first experimental evidence for scaling exponent saturation in longitudinal velocity increments, and is consistent with a dominance of localized vortex filaments in turbulence.

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physics.flu-dyn 2026-05-04

Local entropic scheme recovers full anisotropic advection-diffusion

Entropic lattice Boltzmann method for general anisotropic advection--diffusion

Tensorial flux relaxation and corrected stabilizer enable stable simulation of rotated tensors with contrasts up to 10,000:1.

abstract click to expand

Many transport processes exhibit direction-dependent diffusion, described macroscopically by the full-tensor anisotropic advection--diffusion equation (ADE). Numerical discretization is demanding when the principal axes are rotated relative to the mesh, since mixed derivatives and oblique fluxes amplify grid-orientation errors under large tensor contrasts. This paper develops a local entropic lattice Boltzmann discretization for the general anisotropic ADE. The non-equilibrium population is split into a first-order flux sector and a residual ghost sector. The diffusion tensor is imposed through local tensorial relaxation of the flux, while higher-order kinetic content is controlled by an ADE-corrected entropic stabilizer with positivity fallback. Chapman--Enskog analysis shows the scheme recovers the target full-tensor equation with a discrete-time diffusivity relation between the physical tensor and the flux-relaxation matrix. The update is local, matrix-free, and applies to rotated, spatially varying, heterogeneous, and dynamically coupled tensor transport. We validate it on 3D benchmarks--advected Gaussian plumes, decay of rotated Fourier modes, and source-driven transport with varying tensors--covering off-diagonal diffusion, high-P\'eclet advection, anisotropy ratios of O(104)O(10^4) O(104), and local contrasts up to $3\times10^4:1$. It is then applied to orientation-induced Taylor dispersion of Brownian rods, quantifying enhancement from shear-driven rotation. Heat-conduction tests include rotated thermal-conductivity measurements and effective conduction in heterogeneous porous media with anisotropy up to $10^4:1. Finally, anisotropic Rayleigh--B\'enard convection is simulated to examine how plume morphology and heat transfer change over seven decades of anisotropy ratios, demonstrating an accurate, stable local solver for strongly anisotropic advection--diffusion.

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physics.flu-dyn 2026-05-04

Algorithm locates reflectionless shallow-water waves with varying depth and current

Traveling surface wave propagation on shallow water with variable bathymetry and current

The Laplace cascade method determines bathymetry and current profiles that let wave energy travel long distances without reflection or loss.

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Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with virtually no reflection or scattering. By application of the Laplace cascade method for integrating second-order hyperbolic equations, a general algorithm for finding the parameters of inhomogeneous reflectionless flows is proposed. The algorithm is applied to the problem of long linear surface waves propagation in a channel with variable cross-section. The general analysis of the problem is illustrated by a few representative solutions and compared with the results of previous studies. The results obtained may be of interest to mitigate the possible impact of waves on ships, marine engineering constructions, and human coastal activities.

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physics.flu-dyn 2026-05-04

Surface shear viscosity leaves concentric droplet velocity unchanged

Effects of surface viscosities on the motion of a droplet enclosing a translating particle

Dilatational viscosity and eccentricity jointly modify the induced motion of a droplet enclosing a particle.

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We investigate the influence of interfacial rheology on the motion of a compound particle consisting of a viscous droplet enclosing a translating rigid particle in the Stokes flow regime. The droplet interface is modeled using the Boussinesq-Scriven constitutive law, incorporating both surface shear and dilatational viscosities. An exact analytical solution is derived for the concentric configuration, and the analysis is extended to eccentric geometries using a spectral boundary integral method, enabling a systematic examination of confinement, viscosity contrast, and interfacial properties. For concentric configurations, we show that the induced droplet velocity is independent of surface shear viscosity, while surface dilatational viscosity can either enhance or suppress the droplet motion depending on the interplay between confinement and viscosity ratio. This behavior is rationalized in terms of competing effects between reduced interfacial mobility and increased driving force required to maintain the prescribed particle speed. In contrast, when the particle is eccentrically positioned within the droplet, a dependence on surface shear viscosity emerges, leading to a consistent enhancement of droplet motion that becomes more pronounced with increasing eccentricity. The analytical and numerical results are in excellent agreement and reveal how interfacial rheology, confinement, and symmetry breaking jointly govern the dynamics of compound particle systems. These findings provide mechanistic insight and establish a quantitative benchmark for future studies of active compound particles with complex interfaces.

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physics.flu-dyn 2026-05-04

η-grid cuts DNS points to 10% of standard grids at Re=6000

Leveraging unstructured grids for direct numerical simulations of wall turbulence

Tying wall-normal and spanwise spacing to the local Kolmogorov scale outside a thin inner layer preserves accuracy while improving scaling.

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We formulate an unstructured grid-generation framework for direct numerical simulations (DNSs) of wall turbulence, termed {\eta}-grid, based on setting the wall-normal (y) and spanwise (z) grid sizes proportional to the local Kolmogorov scale {\eta}. The framework consists of an inner layer, with a thickness ~50 viscous units, with viscous-scaled grid sizes similar to a conventional DNS grid; 0.3 < {\Delta}y+ < 4, {\Delta}z+ ~ 5 over a smooth wall, and l+/30 < {\Delta}y+, {\Delta}z+ < 4 over a non-smooth surface, where l+ is the smallest surface wavelength. Above the inner layer, {\Delta}y+~ {\Delta}z+ ~ 2{\eta}+. We test {\eta}-grid with a finite volume method (FVM) code, as well as a spectral element method (SEM) code, and conduct a campaign of DNSs of turbulent channel flow and turbulent boundary layer over smooth wall and various riblet geometries (as streamwise-aligned microgrooves), up to friction Reynolds number {\delta}+0= 1000. We assess the accuracy of the {\eta}-grid against the conventional Cartesian grids, as well as the reference DNS and experimental data. We obtain less than 1% difference between the {\eta}-grid and the Cartesian grids, in terms of skin-friction coefficient, mean velocity, turbulent stresses, and their spectrograms. Up to {\delta}+0 ~ 104, the number of grid points with the {\eta} -grid (N{\eta}) scales proportional to {\delta}+02.5 over smooth wall, and proportional to {\delta}+02.0 over riblets, whereas the number of grid points with a Cartesian grid and hyperbolic tangent y-gird (NTanh) scales proportional to {\delta}+03.0. This leads to an enormous grid saving with the {\eta}-grid; by {\delta}+0 = 6000, N{\eta} / NTanh ~ 0.1 over smooth wall, and N{\eta} / NTanh ~ 0.03 over typical drag-reducing triangular riblets with tip angle 60o, and viscous-scaled spacing 15.

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physics.flu-dyn 2026-05-04

ALE correction enables stable ML predictions for fluid-structure flows

An ALE-Consistent Graph Neural Operator-Transformer Framework for Fluid-Structure Interaction

Graph neural operator and transformer model fluid motion while LSTM tracks structure, with velocity matching at interfaces yielding accurate

abstract click to expand

We propose an arbitrary Lagrangian-Eulerian (ALE)-consistent machine learning framework for long-term fluid-structure interaction (FSI) prediction on deforming unstructured meshes. Specifically, the fluid dynamics are modeled by a surrogate that combines a graph neural operator (GNO) with a vision Transformer (ViT) for spatiotemporal prediction, while a lightweight long short-term memory (LSTM) network predicts structural kinematics at the interface. The two surrogates are coupled through a standard partitioned procedure. Most importantly, kinematic compatibility at the moving interface is enforced via an ALE-consistent boundary-correction step that updates the fluid-side interface velocity with the predicted structural velocity at each coupling update, thereby improving near-interface accuracy and long-term rollout stability. To mitigate autoregressive error accumulation, a two-stage training strategy is adopted, consisting of single-step supervised pretraining followed by long-term autoregressive fine-tuning. The proposed framework is validated on the benchmark problem of a flexible beam vibration in the wake of a cylinder. Results demonstrate accurate phase-consistent predictions over long rollouts and robust generalization under inlet-profile variations in both interpolation and extrapolation settings. Systematic ablation studies further assess the respective contributions of the ViT module, ALE-consistent boundary correction, and long-term training to predictive accuracy and rollout robustness.

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physics.flu-dyn 2026-05-04

Buoyancy anomaly drives three phases of finger convection growth

Dynamics of finger-type convection in double-diffusive instability

Experiments and simulations link increasing then diluting buoyancy to acceleration, steady propagation, and late deceleration in double-diff

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Finger-type convection in double-diffusive instability (DDI) controls mixing and scalar transport in many stratified flows, yet a quantitative, finger-resolved description of the transient growth, transport, and saturation pathways has been limited. Here, finger-type DDI is analyzed in a sealed-surface laboratory facility using synchronized planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) at fixed thermal contrast $\Delta T=5^\circ$C and three salinity contrasts, $\Delta S=350$, 450, and 550 ppm, complemented by a matched high-resolution three-dimensional DNS. A systematic fingertip detection and tracking framework generates ensemble growth curves. Fingertip growth follows a sequence of three stages (acceleration, quasi-steady propagation, and decay). The peak growth rates increase monotonically with $\Delta S$, and nondimensional fingertip-height histories collapse onto a common trend. The peak growth rates are reproduced by DNS and agree with linear stability analysis, establishing experiment--DNS--theory consistency in the intermediate regime. The mixed-material area increases with time, initially following a common nondimensional trend before transitioning to $\Delta S$-dependent interaction and breakdown. Finger-scale measurements reveal the formation of a symmetric vortex ring at the fingertips for $\Delta S=450$ ppm, inducing vertical-aligned transport. At $\Delta S=550$ ppm the roll-up becomes asymmetric: stronger buoyancy amplifies shear, destabilizes the vortex ring, and produces a zig-zag/lateral-drift mode that enhances the lateral transport. Finally, the evolution of the buoyancy anomaly links the growth-rate phases to a time-dependent force balance in which increasing buoyancy drives acceleration, shear-induced resistance regulates quasi-steady propagation, and dilution with top-boundary influence yields late-stage fingertip deceleration.

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physics.flu-dyn 2026-05-04

Navier slip matches microscale velocity acceleration at contact lines

The rapidly advancing contact line Part-1: Navier slip and microscale inertial effects

Local inertia outside the slip zone explains observed interface speed-up down to tens of micrometers in curtain coating.

abstract click to expand

Curtain coating, in which a moving plate is coated by a falling liquid sheet, sustains advancing contact lines at large capillary numbers Ca ~ O(1), based on plate speed. Steady states exist up to a critical capillary number, beyond which wetting failure occurs through air-bubble entrainment. In the steady regime, experiments report that velocity along the fluid-fluid interface accelerates as the contact line is approached, down to tens of micrometres; this has been interpreted as evidence against the Navier slip model. We ask whether this acceleration is compatible with slip models, and show that it is. Although Navier slip implies a vanishing velocity at the contact line, the experimentally accessible microscale region lies outside the slip region. The curtain-coating setup is revealing because the local Reynolds number, based on distance from the contact line r ~ 10 microns, is order unity, so the observable flow is governed by local inertia. Our two-phase Navier-Stokes Volume-of-Fluid simulations with quadtree adaptive mesh refinement resolve the smallest scales and study the flow with a Navier slip boundary condition and fixed contact angle. The simulations reproduce the non-monotonic dependence of the critical capillary number on global Reynolds number, based on feed-flow velocity, and the variation of the macroscopic contact angle at the inflection point, in agreement with Liu et al (2016). The interfacial velocity in the microscale region is well described by an inertially corrected wedge flow solution whose wedge angle is set by the inflection-point value, with agreement improving as slip length is reduced; at larger scales, interface bending follows the Benney solution. These inertial effects, absent from pure Stokes flow, are essential in the experimental region. Thus qualitative microscale observations do not decisively invalidate slip models for advancing contact lines.

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physics.flu-dyn 2026-05-01

Realistic flows weaken wave frequency spreading tenfold

Frequency spreading of internal wave energy by balanced flows in two dimensions

Two-dimensional turbulent simulations cut diffusion rates by an order of magnitude versus synthetic flows and narrow the gap to three-D理论.

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Interactions between inertia-gravity waves and balanced flows lead to a spectral diffusion of wave action. Prior work has established that this diffusion is weak across constant frequency surfaces in three-dimensional settings, but can be significant in two dimensions with a non-stationary balanced flow. We investigate the two-dimensional setting through numerical simulations that simultaneously evolve a turbulent quasigeostrophic balanced flow and advect rotating shallow water wave packets. In contrast to earlier predictions based on the synthetic flows used by Dong et al. (J. Fluid Mech., 2020, vol. 905, R3), we find that frequency spreading from wave mean-flow interactions is weaker for realistic turbulent flows. We derive a timescale for frequency diffusion and show that frequency spreading with a realistic background flow is an order of magnitude smaller than with the synthetic flow. We narrow the discrepancy between the two- and three-dimensional induced diffusion theories, which suggests other mechanisms are responsible for the broadband frequency spectra seen in the atmosphere and ocean.

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physics.flu-dyn 2026-05-01

Curved menisci shift sloshing frequencies in microgravity tanks

Curvature-corrected sloshing spectra for cylindrical tanks in microgravity

When Bond numbers reach order one, flat-surface models miss the mode coupling and frequency changes relevant to spacecraft propellant tanks.

abstract click to expand

In microgravity, a partially filled cylindrical tank is generally bounded by a curved equilibrium meniscus rather than by an almost flat free surface. This modifies both the bulk liquid inertia and the capillary restoring force, so flat-interface sloshing frequencies can become inaccurate even in the linear regime. This effect matters once the Bond number is of order unity or smaller, precisely the regime relevant to capillarity-dominated propellant management. This study revisits the classical cylindrical curved-meniscus eigenvalue problem for capillary-gravity sloshing about axisymmetric Young-Laplace equilibria. A semi-analytical boundary-operator formulation is derived that preserves the cylindrical Bessel structure and recovers the flat-interface limit exactly. Its main advantage lies in treating the bulk Dirichlet-Neumann operator and the linearised curvature operator as distinct components, thereby making the physical origin of curvature-induced frequency shifts explicit. The results show that equilibrium curvature couples radial modes and alters the low-order spectrum once $Bo \lesssim 1$. Concave menisci lower the fundamental frequency, whereas convex menisci raise it while often lowering higher branches. The asymmetry between wetting and non-wetting configurations is found to be predominantly kinetic, being carried mainly by the Dirichlet-Neumann operator rather than by the capillary term. Curved menisci should therefore be treated as part of the leading-order model of cylindrical microgravity sloshing, not as a secondary correction, if reduced-order predictions are to capture the relevant dynamical scales for spacecraft applications.

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physics.flu-dyn 2026-05-01

Merging identical phases fixes unique free-energy closure for N-phase models

Mixture-aware closure of the N-phase Navier--Stokes--Cahn--Hilliard mixture model

A small set of axioms plus PDE-level invariance under phase merging determines the admissible free-energy and mobility forms, including the

abstract click to expand

Diffuse-interface (phase-field) models are widely used to describe multiphase mixtures and their interfacial dynamics. In multiphase settings, however, the constitutive closure should remain meaningful across different representations of the same mixture. Existing N-phase phase-field constructions commonly enforce reduction only when a phase is absent (restriction to a face of the Gibbs simplex), but do not address the natural requirement that physically identical phases can be merged without changing the governing equations. This requires characterizing thermodynamically admissible, mixture-aware constitutive closures that are consistent with merging identical phases at the PDE level. Here, we show that, under a small set of structural axioms, PDE-level reduction consistency uniquely fixes the admissible free-energy structure to an ideal-mixing contribution to an ideal-mixing contribution, a symmetric mean-field interaction term, and a constant-coefficient quadratic gradient penalty. yielding a thermodynamic closure that includes Maxwell--Stefan-type mobilities as a special case. The same requirement constrains the Onsager mobility matrix to a pairwise-exchange form with bilinear degeneracy in the volume fractions, yielding a thermodynamic closure that includes Maxwell--Stefan-type mobilities as a special case. These results provide a consistent closure for N-phase Navier--Stokes--Cahn--Hilliard mixture models and, in the bulk-only setting, for multiphase Maxwell--Stefan diffusion systems. Numerical experiments confirm the predicted mixture-aware reduction properties and illustrate the capabilities of the N-phase Navier--Stokes--Cahn--Hilliard framework in representative multiphase-flow computations.

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physics.flu-dyn 2026-05-01

Heterogeneity speeds gravity currents but reduces dissolution

Mixing and spreading of gravity currents in heterogeneous porous media

Simulations show convection narrows interfaces in unstable cases and homogeneous media dissolve more except at low Rayleigh numbers

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We analyze the mixing, migration and spreading of a gravity current in a heterogeneous porous medium using high-fidelity numerical simulations. Heterogeneity is represented by log-normal permeability fields of varying correlation lengths and variance. Stable and unstable density stratification scenarios are considered through linear and non-monotonic density laws, respectively. Heterogeneity reduces dissolution and increases the speed of the gravity current proportionally to the Rayleigh number. In the unstable case, heterogeneity accelerates the onset of convection. Convection-driven dissolution slows down the gravity current and counteracts the dispersive effect of heterogeneity resulting in a narrower interface and higher dissolution than in the stable case. Permeability anisotropy reduces dissolution because of the barrier effect of low permeability regions, except when blobs of buoyant fluid are trapped in low permeability structures and rapidly dissolve. The variance of the log-permeability field enhances dissolution. However, the homogeneous case outperforms heterogeneous cases except when Rayleigh number is small. This suggest an interaction between the size of the instabilities, the correlation length of the permeability field and the dispersive and barrier effects of the permeability field that controls dissolution efficiency.

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physics.flu-dyn 2026-05-01

Calibrated phase field model matches molecular dynamics for contact lines

Cahn-Hilliard Phase Field modelling captures nanoscale contact line dynamics on high-friction surfaces

Fitting friction to angle evolution yields accurate interface curvature and flow structure.

abstract click to expand

Incorporating molecular-scale effects in the description of contact line motion is essential for accurately capturing all sources of energy dissipation in wetting dynamics. This holds particularly true in the cases where contact line friction dominates, and hydrodynamics models struggle to achieve regularisation due to the negligible Navier slip. We perform Molecular Dynamics simulations of water/hexane biphasic systems in a two-phase Couette flow configuration. Wetting occurs over a silica-like surface with controllable wettability. The simulation results are reproduced by a Phase Field model (Cahn-Hilliard Navier-Stokes equations), which includes localised contact line slip and contact angle dynamics. The continuous equations are directly parametrized from Molecular Dynamics simulation results, under the numerical sharp interface limit. We demonstrate that the Phase Field model can quantitatively reproduce Molecular Dynamics through a systematic calibration protocol. Critically, we show that contact line friction is the primary physical parameter requiring empirical calibration based on Molecular Dynamics data. Once extracted by matching contact angle dynamics, quantitative agreement across multiple observables is obtained, including interface curvature, steady contact line displacement, and the structure of streamlines. All other model parameters are determined a posteriori, according to the calculation of independent observables and under numerical constraints. The results presented in this article indicate that Phase Field modelling can capture the net effect of molecular processes on the mobility of contact lines and that the careful calibration of contact line friction based on the reconstruction of contact angle dynamics and interface bending is key to fully reconcile continuous models with Molecular Dynamics.

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physics.flu-dyn 2026-05-01

One plane of PIV data reconstructs 3D stall cells

To stall-cell or not to stall-cell: Variational data assimilation of 3D mean flow past a stalled airfoil

Variational assimilation blends sparse measurements with RANS prior to recover counter-rotating vortices on post-stall airfoil.

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The full-field reconstruction of three-dimensional (3D) turbulent flows from sparse experimental measurements remains a significant challenge, particularly for flows exhibiting complex 3D flow separation. In this work, we address this challenge for the case of stall cells - spanwise coherent structures that form on the suction surface of wings at post-stall conditions. Planar particle image velocimetry (PIV) experiments are performed on a NACA 0012 wing at a chord-based Reynolds number of $Re_c \approx 450{,}000$ and angle of attack $\alpha = 14^\circ$, acquiring two-component mean velocity data on four spanwise planes. The experimental data show clear spanwise variation in the extent of the separation and flow dynamics, consistent with the presence of stall cells. Three-dimensional variational (3DVar) data assimilation (DA) within the field inversion framework is then employed to reconstruct the full 3D mean flow field by augmenting these sparse planar measurements with the Spalart--Allmaras (SA) Reynolds-averaged Navier--Stokes (RANS) turbulence model. The performance of the reconstruction is assessed on planes not used in the assimilation. It is shown that a single plane of sparse experimental data is sufficient to recover the essential features of a stall cell, including counter-rotating vortices around focal points on the suction surface. The lowest reconstruction error is obtained when two planes of data that are close together but exhibit markedly different separation extents are used, and the complementary roles of the reference data placement and the computational boundary conditions in shaping the reconstructed stall cell structure are explained. These results demonstrate the capability of 3DVar DA to reconstruct the full 3D physics of stall cells from two-component velocity data acquired on select spanwise planes.

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physics.flu-dyn 2026-05-01

Early sliding shapes asymmetric ice on inclined surfaces

Asymmetric freezing of a sliding droplet on an inclined surface

Simulations show gravity-driven motion before and during initial freezing creates tilted cusps whose size depends on inclination and wettabi

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We investigate the asymmetric freezing of a liquid droplet sliding on an inclined cold surface using numerical simulations based on the lubrication approximation. The combined effects of gravity, capillarity, and solidification kinetics on droplet motion, interfacial deformation, and the resulting frozen morphology are examined through systematic variations in substrate inclination, wettability, effective Bond number, and Stefan number. Our results show that sliding prior to and during the early stages of freezing plays a dominant role in governing the asymmetry of the frozen droplet. A tilted ice cusp forms at the droplet tip due to the competition between gravitational forces and capillary resistance, with its orientation and magnitude strongly dependent on substrate wettability and inclination. Greater inclination and increased wettability enhance asymmetry in droplet morphology. Further, highly wetting substrates favor capillary-driven retraction and induce transient liquid motion opposite to gravity during freezing. The evolution of contact-angle hysteresis at both the solid surface and the liquid-ice interface underscores the importance of early-time dynamics, when the unfrozen liquid remains mobile and gravitational effects are most pronounced. Decomposition of the liquid motion into capillary and gravity-driven contributions provides physical insight into contact-line pinning, receding-edge thinning, and the development of asymmetric liquid-ice contact angles. Increasing the Stefan number accelerates freezing, limits sliding-induced deformation, and reduces both the cusp angle and the post-freezing contact-angle contrast. Overall, this study establishes a physical framework for understanding the morphology of frozen droplets on inclined substrates.

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physics.flu-dyn 2026-04-30

Particle kinetic energy alone trains turbulence sub-grid models

Training of particle-turbulence sub-grid-scale closures with just particle data

Neural networks learn effective stress closures from noisy or partial particle velocity data without flow-field input.

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If sufficient training data are available, neural networks are attractive for representing missing physics in simulations, such as sub-grid scales in the coarse-mesh particle-turbulence system we consider. Physical constraints are known to both increase performance and reduce the need for data; we use the complete physics represented in the discretized governing equations as a constraint. Two-way coupled particles in two-dimensional turbulence provide a sufficiently complex system to assess effectiveness for various training data, all constructed from well-resolved simulations, in cases intentionally degraded to assess robustness. Surprisingly, using the full space-time data actually hinders model effectiveness. Instead, training that targets only spectra -- hence, neglecting phase information -- provides better closures, which is related to the well-known success of non-dissipative discretizations for simulating turbulence. It is found that some of the missing physics that lead to preferential particle concentration errors are fundamentally stochastic on the coarse mesh and therefore uncorrectable by the basic approach; a learning formulation is introduced for a Langevin-type closure to correct this. Most importantly, training just for particle kinetic energy -- without any direct input from the flow field -- also yields effective sub-grid-scale stress models. This holds true even if noise is added to the particle data, if only a sub-sample of particles are used, or if only one component of the particle velocity is used. In sum, these results show a path for inferring sub-grid-scale physics based just on particle data from experiments.

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physics.flu-dyn 2026-04-30

Hybrid neural operator speeds lattice Boltzmann flows by 70 percent

Hybrid Fourier Neural Operator-Lattice Boltzmann Method

FNO initialization and rollouts cut convergence time for steady states and stabilize long unsteady predictions while preserving accuracy.

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We propose an accelerated computational fluid dynamics framework based on a hybrid Fourier Neural Operator-Lattice Boltzmann Method (FNO-LBM) for steady and unsteady weakly compressible flows. FNO-based initialization significantly accelerates LBM in reaching steady-states of porous media flows across all macroscopic fields, achieving up to 70% speed-up in convergence of density and more than 40% of pressure-drop while preserving the final steady-state accuracy. Simulations of unsteady flows can be accelerated by hybrid coupling strategies that employ FNO rollouts embedded into LBM time advancement in a way of super-time-stepping. Global and time-resolved error metrics across 100 trajectories for generic 2D flows demonstrate that hybridization consistently improves accuracy and stabilizes long-horizon rollouts. Best efficiency is achieved for a lightweight 2.6M-parameter FNO, which diverges under pure autoregressive rollout but achieves 96-99.8% error reduction under hybrid coupling, matching the predictive capability of a much more expensive 11.2M-parameter model. The hybrid framework enhances predictive fidelity, suppresses error accumulation, and enables small and cheap surrogate models to operate effectively within the same error regime as larger surrogates. These results demonstrate that hybrid neural-operator coupling achieves robust and computationally efficient accelerated LBM while maintaining physically consistent flow evolution.

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physics.flu-dyn 2026-04-30

Compressible Navier-Stokes recast in Schrödinger variables

Compressible Navier--Stokes Flow in Schr\"odinger-Type Variables

Exact Cole-Hopf mapping turns isothermal flow into imaginary-time equations, nonlocal only through projections and verified on shear-layer

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Fluid equations are nonlinear, dissipative, and non-Hamiltonian, which makes their relation to Schr\"odinger evolution and quantum algorithms nontrivial. We derive an exact Eulerian Cole-Hopf-type reformulation of isothermal compressible Navier-Stokes (NS) flow in Schr\"odinger-type amplitude variables. To our knowledge, this gives the first exact Cole-Hopf-type Schr\"odinger-variable reformulation of compressible NS flow. In two dimensions, a Helmholtz decomposition separates the velocity into compressive and vortical potentials, whose logarithmic transforms yield two scalar imaginary-time Schr\"odinger-type equations with nonlinear self-consistent potentials. We show that the mixed density-compressive amplitude $\Psi_\alpha=\rho^\alpha\Theta^{1-2\alpha}$, where $\rho$ is the density, $\Theta$ is the compressive amplitude, and $\alpha\neq 0,\,1/2$, satisfies a nonlinear Schr\"odinger-type equation with a vector-potential-coupled Laplacian. The transformed system is exactly equivalent to compressible NS and is nonlocal only through Helmholtz and Poisson projections. In three dimensions, the density-carrying equation retains the same vector-potential-coupled structure, while the solenoidal sector admits a compressible analogue of Ohkitani's incompressible NS Cole-Hopf formulation. Unlike unitary hydrodynamic Schr\"odinger-flow representations, the present equations are imaginary-time heat or drift-diffusion equations with self-consistent potentials, but they remain an exact change of variables for compressible NS. A two-dimensional Kelvin-Helmholtz unstable shear-layer calculation verifies the transformed equations against a direct compressible NS simulation. The formulation exposes operator structures that may be useful for reduced flow descriptions, quantum algorithms for operator evolution, and quantum partial differential equation solvers.

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physics.flu-dyn 2026-04-30

Temperature-dependent Korteweg stresses couple mechanics and heat

Constitutive Modelling of Korteweg Fluids Using Liu's Method

Liu's method produces a generalized Gibbs relation with capillary effects while matching kinetic-theory predictions.

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The paper studies constitutive modelling of Korteweg fluids. Thermodynamic consistency, i.e. compatibility with entropy balance law, is achieved using Liu's method of multipliers. Appropriate constitutive assumptions facilitated inclusion of the capillary effects in the specific entropy. Korteweg stresses are derived from the equilibrium conditions -- vanishing of the entropy production and its minimization in equilibrium. Material parameter in Korteweg stresses is allowed to depend on temperature, which turns out to be consistent with kinetic-theory results and leads to cross-coupling of mechanical and thermal effects. The generalized Gibbs' relation, which inherits the capillary effects, is derived as consequence, which is a peculiar feature of the Liu's method.

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physics.flu-dyn 2026-04-30

Diffusion model upsamples coarse wind turbulence to fine detail

Conditional diffusion denoising probabilistic model for super-resolution of atmospheric boundary layer large eddy simulation

Conditional diffusion recovers structures and stresses accurately inside training conditions but overpredicts noise at higher wind speeds.

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Climate change necessitates rapid expansion of renewable energy, with wind energy offering a scalable and low-impact solution. However, accurate prediction of wind loads and power generation remains challenging due to uncertainties in wind shear and turbulence stresses under atmospheric boundary layer (ABL) conditions. High-fidelity Large Eddy Simulations (LES) are typically used to reduce these uncertainties but are computationally expensive and impractical for large-scale or real-time applications. This work addresses this limitation using generative AI, specifically Conditional Denoising Diffusion Probabilistic Models, to reconstruct high-resolution turbulent flow fields from coarse inputs. A high-fidelity dataset is generated using a parallel high-order finite-difference solver across varying geostrophic wind speeds, surface roughness conditions aligned with IEC wind classes, and multiple grid resolutions. The diffusion model is trained for super-resolution across different scale factors and evaluated under interpolation and extrapolation scenarios. Results show accurate recovery of fine-scale turbulent structures, Reynolds stresses, and statistical properties in interpolation cases, indicating strong physical consistency within the training domain. However, extrapolation to higher wind speeds leads to increased noise and overprediction of turbulent stresses, highlighting limitations in generalization. Overall, the study demonstrates that physics-informed generative models can significantly reduce computational cost while maintaining acceptable accuracy, enabling faster and more reliable turbulent inflow characterization for wind energy applications.

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physics.flu-dyn 2026-04-30

Clustering CFD data creates accurate fast compartment models

Compartment Modelling of Multiphase Reactors using Unsupervised Clustering

Unsupervised grouping plus graph fixes yields reduced reactor models that match full simulations while enabling real-time control.

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Detailed Computational Fluid Dynamics (CFD) simulations are too computationally expensive for the real-time control and design optimization of multiphase flow reactors. To address these limitations, we introduce CLARA, a software toolbox that automates the generation of Compartment Models (CM) via the unsupervised clustering of CFD data. Unlike previous studies, our toolbox enables the modelling of multiphase phenomena and interphase mass transfer within each compartment. CLARA employs unsupervised clustering algorithms, graph reassignment, and optimization routines to ensure mass conservation and spatial connectivity across all compartments. Verification studies utilizing analytical benchmarks and reactive multiphase CFD simulations demonstrate that the CMs produced by CLARA accurately reproduce reactor performance and spatial species distributions. The significantly reduced computational demand of CMs compared to full CFD models enables the optimal control of multiphase reactors and facilitates their rational design and optimization.

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physics.flu-dyn 2026-04-30

Phase difference controls vortex direction at oscillating holes

Wave Vortices Around Oscillating Subwavelength Holes: Water-Wave Observation

In water-wave experiments, adjusting timing between an island's oscillation and incoming waves determines if and which way type-II vortices

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We consider a two-dimensional wave system containing a subwavelength hole, such as an aperture in an interface supporting surface electromagnetic or acoustic waves, or an island in a fluid surface sustaining gravity-capillary waves. Recent studies have revealed the emergence of pronounced wave vortices around such structures, termed type-II vortices, in contrast to conventional (type-I) vortices associated with phase singularities and intensity nulls. A striking natural manifestation of type-II vortices occurs in ocean tides around islands such as New Zealand, Madagascar, and Iceland, where the tidal phase increases by $\pm 2\pi$ around the island. Although this phenomenon is usually associated with the Coriolis effect from the rotation of the Earth, here we demonstrate the controlled generation of type-II vortices using a minimal and tunable setup: a dipole-oscillating subwavelength hole and a single incident plane wave. Using laboratory gravity-capillary waves and an oscillating subwavelength `island', we directly measure the resulting phase structure, topological charge, and wave angular momentum. We show that the emergence and handedness of the vortices can be precisely controlled via the relative phase between the dipolar source and the incident wave. Our results offer a simple and versatile mechanism for engineering subwavelength wave vortices, with potential applications in a variety of two-dimensional wave systems.

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physics.flu-dyn 2026-04-30

Neural operator matches LES accuracy for wall turbulence

Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence

LESnets embeds large-eddy equations and wall law into a Fourier model to predict channel flows without any training data.

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Accurate and efficient prediction of three-dimensional (3D) wall-bounded turbulent flows poses a significant challenge for machine learning methods, particularly in scenarios where flow field data are limited. Physics-informed neural operator (PINO) combines neural operator and physics constraint methods, and shows great potential for solving a wide range of partial differential equations. Nevertheless, the multi-scale vortex structures in wall-bounded turbulence make it difficult for most existing PINO methods to make stable and accurate long-term predictions at high Reynolds numbers. To address this challenge, we develop the large-eddy simulation nets (LESnets) that integrates large-eddy simulation (LES) equations into the factorized Fourier neural operator (F-FNO) for wall-bounded turbulence. The LESnets framework does not rely on labeled data for training, which enables it to generate temporal solutions over flexible time horizons during the training process. Moreover, the law of the wall is integrated into the LESnets framework through a wall model for the physics-informed loss, thus enabling reliable simulations of wall-bounded turbulence at high Reynolds number using coarse grids. The proposed LESnets methods are demonstrated in turbulent channel flows at three friction Reynolds numbers: 180, 590, and 1000. Numerical experiments show that the performance of the LESnets in terms of prediction accuracy and efficiency is comparable to that of two data-driven models, namely the implicit U-Net enhanced Fourier neural operator (IUFNO) and F-FNO. Meanwhile, the LESnets model achieves prediction accuracy comparable to traditional LES methods while offering a higher computational efficiency. Thus, the LESnets model demonstrates strong potential for efficient and long-term prediction of wall-bounded turbulent flows.

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physics.flu-dyn 2026-04-30

Multi-jet RL control raises airfoil efficiency from 53 to 73 percent

A Provably Robust Multi-Jet Framework applied to Active Flow Control of an Airfoil in Weakly Compressible Flow

The formulation removes redundant jet actions and keeps maximum costs constant no matter how many jets are used.

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Reinforcement learning has by now become well established in finding excellent flow control strategies for a variety of scenarios. Existing literature has focused on using a simple two-jet solution (and variants there-of) or a straightforward mean-centered multi-jet setup. This mean-centering approach is however non-injective in nature, such that distinct action predictions by the actor network can lead to the same implemented jet-intensities. Thus, the potential of true multi-jet setups still remains unexplored. To this end, in this study we first theoretically analyze multi-jet setups, highlighting the aforementioned pitfall and offer a viable alternative. We also derive upper-bounds on the running costs of these setups, and find the proposed approach to have a jet-count-independent maximum running cost (compared to a near-linear scaling for the traditional setup). The mean-centered and proposed multi-jet setups are applied to a variety of flow-configurations, to test performance and learning capabilities. The new formulation proves effective in learning more complex flow-control strategies, coordinating the jets in a sophisticated manner so as to produce favorable outcomes at minimal actuation cost. For the cylinder-in-channel case, this results in drag and total-force suppression to beyond an idealized symmetric case, whereas for the airfoil the separation region is minimized and significant improvements in aerodynamic efficiency are observed (from 53% up to 73% depending on jet configuration). Additionally, we also incorporate some best practices from traditional RL literature to show fast, reproducible and reliable learning, thereby bringing down the upfront training costs. This study thus provides a robust and mathematically grounded approach to multi-jet design and closes a hitherto overlooked theoretical gap.

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