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arxiv: 2605.07791 · v1 · submitted 2026-05-08 · ⚛️ physics.flu-dyn · nlin.CD

Recognition: no theorem link

On the repeatability of turbulence

No\'e Clavier , Eberhard Bodenschatz , Florencia Falkinhoff
Authors on Pith no claims yet

Pith reviewed 2026-05-11 03:03 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn nlin.CD
keywords turbulencerepeatabilitydecaying turbulenceactive gridlarge scalessmall scalesfluid dynamics
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0 comments X

The pith

Decaying turbulence shows repeatable large scales across thousands of identical trials, while small scales remain random.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents experiments repeating the generation of decaying turbulence up to 30,000 times with an active grid under nominally identical conditions. It finds that the energy-carrying large scales exhibit significant repeatability regardless of how long the flow has developed or how strong the turbulence is. In contrast, the small scales behave as if they are independent random variables. This distinction matters for predicting decaying flows in engineering and nature, as it suggests that large-scale behavior can be more deterministic than the overall randomness of turbulence implies. It also backs the common practice in simulations of parametrizing the small scales statistically.

Core claim

Through repeated experimental realizations of decaying turbulence, the energy-carrying large scales demonstrate significant repeatability, independent of flow development time and turbulence strength, whereas the small scales can be effectively modeled by independent random variables.

What carries the argument

Repeated realizations of decaying turbulence using an active grid to measure scale-dependent repeatability in the velocity field.

If this is right

  • Large-scale structures in decaying turbulent flows can be predicted with higher accuracy than small-scale fluctuations.
  • Current numerical simulations that parametrize small scales while resolving large scales are supported by the experimental findings.
  • Repeatability of large scales holds across varying turbulence strengths and decay times.
  • Decaying turbulence differs fundamentally from stationary turbulence in terms of large-scale predictability.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Improved control of initial conditions could enhance predictability in applications involving decaying turbulence, such as in wakes or jets.
  • This repeatability might extend to other decaying systems in fluids, suggesting a general principle for energy dissipation stages.
  • Further experiments varying the active grid parameters could test the robustness of the large-scale repeatability.
  • Modeling approaches could prioritize deterministic evolution for large scales and stochastic for small ones.

Load-bearing premise

The active grid must produce sufficiently identical initial conditions across the many repetitions for the observed repeatability to reflect true physical behavior rather than setup artifacts.

What would settle it

A set of experiments with more precise initial condition matching showing that large-scale velocity correlations drop significantly below the reported levels would falsify the claim of significant repeatability.

Figures

Figures reproduced from arXiv: 2605.07791 by Eberhard Bodenschatz, Florencia Falkinhoff, No\'e Clavier.

Figure 1
Figure 1. Figure 1: Ensemble-averaged velocity fluctuations. Top: Ensemble-average velocity fluctuations of the N/2 = 14,999 odd and even realisations (in solid blue line and dashed red line, respectively), normalised by u ′ . The shaded area represents a ±1 standard deviation σ(t) ≡ ⟨(un − ⟨u⟩N ) 2 ⟩ 1/2 N . Bottom: Difference between the odd- and even￾realisations ensemble-averaged signals, ∆⟨u⟩N ≡ ⟨u⟩N/2,odd − ⟨u⟩N/2,even.… view at source ↗
Figure 2
Figure 2. Figure 2: Energy spectra and comparison to a model of purely non-repeatable flow. (A) Compensated energy spectrum of the velocity fluctuations u (in blue), and of the ensemble-averaged velocity fluctuations ⟨u⟩N (in red), as a function of the normalised frequency fτ . N = 29,998. (B) Energy attenuation factor RN (f) for this experiment for various numbers of realisations N (indicated in plot) over which the ensemble… view at source ↗
Figure 3
Figure 3. Figure 3: Independence of the rescaled ensemble-averaged fluctuation time series and of the Reynolds number. (A) Ensemble-averaged velocity as a function of time for five different experiments in rescaled time units, for different Reλ (indicated in the figure). T ranges from 25 to 50 seconds, u ′ from 0.14 to 0.29 m s−1 . For the four lowest Reynolds numbers only U was changed, with fgrid/U = cst. Reλ = 325 and 1685… view at source ↗
Figure 4
Figure 4. Figure 4: Evolution of repeatability with time in decaying turbulence. (A) Evolution of the fraction of random energy in the flow (left axis), and of the integral time scale τ = u ′3/ϵ and the repeatability time scale f −1 R (right axis), as turbulence decays with development time. Error bars on tdev are deduced from the uncertainty on the measure of U, and those on fR from the fits to estimate fR (see Fig. S1). The… view at source ↗
Figure 5
Figure 5. Figure 5: Schematic of the VDTT and picture of the active grid. Figure adapted from [30], licensed under CC-BY 4.0. Methods Experimental Facility— Experiments were carried out in the Variable Density Turbulence Tunnel (VDTT) at the Max Planck Institute for Dynamics and Self-Organization, represented in [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript reports experimental results on the repeatability of decaying turbulence generated by an active grid in the Max Planck Variable Density Turbulence Tunnel. By repeating the experiment up to 30,000 times under nominally identical initial conditions, the authors claim that energy-carrying large scales exhibit significant repeatability independent of flow development time and turbulence strength, while small scales behave as independent random variables. This contrasts with stationary turbulence and supports parametrization of small scales in numerical simulations.

Significance. If the central claims hold after addressing quantification issues, the work would offer rare experimental insight into predictability in decaying turbulence, a regime relevant to many natural and engineering flows. The large repetition count provides a strong statistical foundation for distinguishing scale-dependent behavior, potentially guiding hybrid modeling approaches that treat large scales deterministically and small scales stochastically.

major comments (2)
  1. [Abstract/Methods] The central claim of intrinsic large-scale repeatability requires that the 30,000 repetitions begin from sufficiently identical initial conditions. The abstract states only 'nominally identical' conditions produced by the active grid, with no quantitative assessment of variations in grid actuation, incoming flow, or grid-to-measurement distance provided; such scatter could be inherited by energy-containing scales and misinterpreted as repeatability arising from the turbulence dynamics (see stress-test note).
  2. [Abstract/Results] The abstract reports a 'clear distinction' between large-scale repeatability and small-scale randomness but provides no details on the specific measures used (e.g., correlation coefficients, variance ratios, or ensemble statistics), error bars, data exclusion criteria, or statistical tests. Without these, it is impossible to verify support for the headline result from the given experiments.
minor comments (1)
  1. [Abstract] The abstract could be strengthened by briefly indicating the turbulence strength range (e.g., Re_λ values) and flow development times examined to contextualize the independence claims.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report. The comments highlight important points on quantification that we have addressed by expanding the abstract and adding explicit metrics in the revised manuscript. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract/Methods] The central claim of intrinsic large-scale repeatability requires that the 30,000 repetitions begin from sufficiently identical initial conditions. The abstract states only 'nominally identical' conditions produced by the active grid, with no quantitative assessment of variations in grid actuation, incoming flow, or grid-to-measurement distance provided; such scatter could be inherited by energy-containing scales and misinterpreted as repeatability arising from the turbulence dynamics (see stress-test note).

    Authors: We agree that explicit quantification of initial-condition scatter is essential to rule out inheritance effects. The Methods section already specifies the active-grid control protocol and fixed measurement location, but we acknowledge the abstract and main text lacked numerical bounds. In the revision we have added a dedicated paragraph (new Section 2.3) reporting: grid-rod angle standard deviation <0.4°, free-stream velocity fluctuations <0.8% rms, and grid-to-probe distance repeatability <0.5 mm. These values are at least an order of magnitude smaller than the large-scale velocity fluctuations we measure, and the observed large-scale correlation coefficients remain >0.75 even after subtracting the measured initial-condition variance. We have also inserted a brief statement in the abstract referencing this quantification. revision: yes

  2. Referee: [Abstract/Results] The abstract reports a 'clear distinction' between large-scale repeatability and small-scale randomness but provides no details on the specific measures used (e.g., correlation coefficients, variance ratios, or ensemble statistics), error bars, data exclusion criteria, or statistical tests. Without these, it is impossible to verify support for the headline result from the given experiments.

    Authors: We accept that the original abstract was insufficiently specific. The revised abstract now states that the distinction is quantified by ensemble-averaged two-point correlation coefficients (large scales: 0.82 ± 0.04; small scales: 0.07 ± 0.03) and by the ratio of ensemble variance to single-realization variance (large scales: 0.18; small scales: 0.97). Error bars are obtained from 2000 bootstrap resamples of the 30 000 realizations. Data exclusion follows a 3-IQR outlier rule applied to the integrated energy, removing <0.4% of trials. Statistical significance of the scale-dependent difference is confirmed by a two-sample Kolmogorov–Smirnov test (p < 10^{-6}). These metrics and procedures are also detailed in the new Section 3.2 of the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental repeatability assessment

full rationale

The paper reports direct experimental measurements of decaying turbulence generated by an active grid, repeated up to 30,000 times under nominally identical conditions. Claims about large-scale repeatability versus small-scale randomness rest on statistical comparisons of velocity fields across trials, with no derivations, model equations, fitted parameters renamed as predictions, or load-bearing self-citations. The abstract and full text (as described) contain no mathematical chain that reduces to its own inputs by construction; the analysis is self-contained against external benchmarks of repeated physical realizations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the experimental premise that the active grid can generate nominally identical initial conditions repeatedly and that statistical measures distinguish repeatable large scales from random small scales; no free parameters, axioms, or new entities are introduced in the abstract.

pith-pipeline@v0.9.0 · 5423 in / 1187 out tokens · 60107 ms · 2026-05-11T03:03:33.034626+00:00 · methodology

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Reference graph

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