The (Limited) Effect of Viscosity in Multiphase Turbulent Mixing

Max Gronke; S. Peng Oh; Tirso Marin-Gilabert

arxiv: 2504.15345 · v2 · pith:UYFWPTUFnew · submitted 2025-04-21 · 🌌 astro-ph.GA · astro-ph.CO

The (Limited) Effect of Viscosity in Multiphase Turbulent Mixing

Tirso Marin-Gilabert , Max Gronke , S. Peng Oh This is my paper

Pith reviewed 2026-05-22 17:59 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO

keywords multiphase gasviscosityturbulent mixingradiative coolingKelvin-Helmholtz instabilitygalactic outflowscircumgalactic medium

0 comments

The pith

In strong cooling regimes required for multiphase gas, viscosity has no effect on turbulence or mixing.

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

The paper examines viscosity in turbulent radiative mixing layers that model multiphase gas in galactic environments. Simulations show viscosity can suppress Kelvin-Helmholtz instabilities and turn flows laminar when cooling is weak. Yet when cooling times are shorter than viscous diffusion times, which must be true for gas to stay multiphase, the system follows the same scaling relations as in the inviscid limit. A reader cares because this limits how much microscopic viscosity needs to be resolved or modeled in galaxy-scale simulations of outflows and the circumgalactic medium.

Core claim

In the strong cooling regime, radiative losses dominate viscous diffusion so that key relations between cooling rate, turbulence, and mixing remain unchanged regardless of the viscosity level present. This holds because the condition for multiphase gas persistence requires cooling timescales shorter than viscous ones, rendering the flow effectively non-viscous.

What carries the argument

Comparison of cooling timescale to viscous diffusion timescale in 2D and 3D shear-layer simulations of turbulent radiative mixing layers.

If this is right

Established inviscid scaling relations between cooling and turbulence remain valid in the strong cooling regime even with viscosity included.
Total luminosity from the mixing layer is unaffected by viscosity in both weak and strong cooling cases.
Subgrid models for large-scale simulations can neglect explicit viscosity when strong cooling is present.
Observational diagnostics of multiphase gas velocities and temperatures can be interpreted without viscosity corrections in strongly cooling environments.

Where Pith is reading between the lines

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

Viscosity can be safely omitted from models of galactic winds and circumgalactic gas where cooling is rapid enough to sustain multiphase structure.
The derived critical viscosity thresholds as function of density contrast and Mach number could be used to set resolution requirements in future simulations.
Adding magnetic fields might change the effective viscosity threshold, providing a testable extension to the current hydrodynamic results.

Load-bearing premise

The numerical viscosity values and idealized shear geometries accurately represent the relative importance of cooling versus viscous diffusion in real astrophysical flows.

What would settle it

A 3D simulation or observation of a strongly cooling shear flow that shows altered mixing rates or broken scaling relations once viscosity is added at levels below the critical KHI-suppression value.

read the original abstract

Multiphase gas can be found in many astrophysical environments, such as galactic outflows, stellar wind bubbles, and the circumgalactic medium, where the interplay between turbulence, cooling, and viscosity can significantly influence gas dynamics and star formation processes. We investigate the role of viscosity in modulating turbulence and radiative cooling in turbulent radiative mixing layers (TRMLs). In particular, we aim to determine how different amounts of viscosity affect the Kelvin-Helmholtz instability (KHI), turbulence evolution, and the efficiency of gas mixing and cooling. Using idealized 2D numerical setups, we compute the critical viscosity required to suppress the KHI in shear flows characterized by different density contrasts and Mach numbers. These results are then used in a 3D shear layer setup to explore the impact of viscosity on cooling efficiency and turbulence across different cooling regimes. We find that the critical viscosity follows the expected dependence on overdensity and Mach number. Our viscous TRMLs simulations show different behaviors in the weak and strong cooling regimes. In the weak cooling regime, viscosity has a strong impact, resulting in laminar flows and breaking previously established inviscid relations between cooling and turbulence (albeit leaving the total luminosity unaffected). However, in the strong cooling regime, when cooling timescales are shorter than viscous timescales, key scaling relations in TRMLs remain largely intact. In this regime -- which must hold for gas to remain multiphase -- radiative losses dominate, and the system effectively behaves as non-viscous regardless of the actual level of viscosity. Our findings have direct implications for both the interpretation of observational diagnostics and the development of subgrid models in large-scale simulations.

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.

Desk Editor's Note private letter to a colleague

Viscosity has little effect on TRMLs in the strong-cooling regime that actually sustains multiphase gas.

read the letter

The main takeaway is that in the strong cooling regime, where radiative losses keep gas multiphase, the mixing layer behaves essentially as if viscosity were absent, even when viscosity is included at levels that would matter otherwise. The paper reaches this by first running 2D shear-flow calculations to pin down the critical viscosity that suppresses the Kelvin-Helmholtz instability across density contrasts and Mach numbers, then feeding those values into 3D turbulent radiative mixing layer runs split by cooling strength. In the weak-cooling case viscosity does change the flow, making it more laminar and breaking some of the usual inviscid scalings between cooling rate and turbulent velocity, though total luminosity is unchanged. In the strong-cooling case the old relations survive, which lines up with the simple timescale comparison t_cool much less than t_visc. This is a clean, incremental step beyond the earlier inviscid TRML literature. The regime separation is handled explicitly and the outcome matches what the timescale argument predicts, so the central result feels grounded rather than forced. The work is useful because it directly addresses when subgrid prescriptions for multiphase gas in cosmological runs can safely ignore viscosity. Soft spots are limited. The abstract states the results clearly, but the absence of visible resolution studies or quantitative plots in the summary makes it hard to judge how cleanly numerical diffusion is separated from the physical viscosity term. The assumption that the chosen viscosity coefficients and idealized geometry capture the dominant timescales is reasonable for this setup, yet real flows include magnetic fields that could alter the effective viscosity; that is a natural next check rather than a flaw in the current work. Readers working on galactic outflows, CGM modeling, or subgrid prescriptions will get the most from it. The new simulation results on viscosity dependence across regimes are substantive enough that the paper deserves a serious referee rather than a desk rejection. I would send it to peer review.

Referee Report

3 major / 3 minor

Summary. The paper uses 2D simulations to determine the critical viscosity needed to suppress the Kelvin-Helmholtz instability (KHI) for varying density contrasts and Mach numbers, then applies these viscosity scales in 3D turbulent radiative mixing layer (TRML) simulations. It reports that viscosity strongly affects the weak-cooling regime (producing laminar flows and breaking inviscid scaling relations between cooling and turbulence), but has negligible effect in the strong-cooling regime where t_cool << t_visc; in that regime the system behaves effectively as non-viscous and preserves established inviscid relations, with direct implications for multiphase gas modeling.

Significance. If the central timescale-separation result holds, the work provides a clear, simulation-backed justification for neglecting viscosity in subgrid models of strong-cooling multiphase gas in galactic outflows and the CGM. The direct numerical approach (2D KHI calibration feeding 3D TRML runs) supplies a falsifiable test of the analytic expectation that radiative losses dominate when cooling is fast, strengthening the case for simplified inviscid treatments in that regime.

major comments (3)

[§3] §3 (2D KHI suppression calculations): the critical viscosity values are stated to follow the expected dependence on overdensity and Mach number, yet no explicit comparison to analytic KHI suppression criteria (e.g., the viscous damping rate versus growth rate) or tabulated values is provided; without this, it is unclear how precisely the viscosity scale inserted into the 3D runs matches the theoretical threshold.
[§4.2] §4.2 (3D TRML runs, strong-cooling regime): the claim that 'key scaling relations remain largely intact' is central to the limited-effect conclusion, but the manuscript does not report quantitative metrics (e.g., measured power-law indices, correlation coefficients, or direct overlays of viscous vs. inviscid cooling-rate vs. velocity relations) that would allow assessment of how small the deviations actually are.
[§4] Throughout §4: while the abstract and text emphasize that the strong-cooling regime must hold for gas to remain multiphase, the simulations do not include a resolution study or explicit demonstration that the chosen grid scale resolves the cooling length relative to the viscous diffusion length at the reported viscosity coefficients; this leaves open whether numerical diffusion could mimic or mask the viscous effect.

minor comments (3)

Figure captions and axis labels in the 3D TRML panels should explicitly state the viscosity coefficient (in code units) and the ratio t_cool/t_visc for each run to make the regime separation immediately visible.
The transition between weak- and strong-cooling regimes is described qualitatively; adding a single plot or table of measured t_cool/t_visc versus viscosity for the 3D suite would strengthen the timescale argument.
A few sentences clarifying the numerical viscosity implementation (e.g., whether it is physical or numerical, and the exact form of the stress tensor) would aid reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and positive report. We address each major comment below and will revise the manuscript to incorporate the suggested improvements where possible.

read point-by-point responses

Referee: §3 (2D KHI suppression calculations): the critical viscosity values are stated to follow the expected dependence on overdensity and Mach number, yet no explicit comparison to analytic KHI suppression criteria (e.g., the viscous damping rate versus growth rate) or tabulated values is provided; without this, it is unclear how precisely the viscosity scale inserted into the 3D runs matches the theoretical threshold.

Authors: We agree that an explicit comparison to analytic criteria would strengthen the presentation. In the revised manuscript we will add a direct comparison of our numerically determined critical viscosities to the analytic expectation (viscous damping rate versus KHI growth rate) and include a table of critical viscosity values together with the ratio to the theoretical threshold for the range of density contrasts and Mach numbers explored. revision: yes
Referee: §4.2 (3D TRML runs, strong-cooling regime): the claim that 'key scaling relations remain largely intact' is central to the limited-effect conclusion, but the manuscript does not report quantitative metrics (e.g., measured power-law indices, correlation coefficients, or direct overlays of viscous vs. inviscid cooling-rate vs. velocity relations) that would allow assessment of how small the deviations actually are.

Authors: We acknowledge that quantitative metrics would better support the central claim. We will revise §4.2 to report fitted power-law indices for the cooling-rate versus velocity-dispersion relations in both viscous and inviscid runs, include correlation coefficients, and add direct overlays or tabulated comparisons showing the magnitude of any deviations. revision: yes
Referee: Throughout §4: while the abstract and text emphasize that the strong-cooling regime must hold for gas to remain multiphase, the simulations do not include a resolution study or explicit demonstration that the chosen grid scale resolves the cooling length relative to the viscous diffusion length at the reported viscosity coefficients; this leaves open whether numerical diffusion could mimic or mask the viscous effect.

Authors: We agree that an explicit demonstration of scale separation would increase confidence in the results. Our resolutions were selected following standard practice in the TRML literature to resolve the cooling length; in the strong-cooling regime (t_cool << t_visc) any unresolved numerical diffusion acts analogously to viscosity yet remains sub-dominant to radiative losses. We will add a concise discussion in the methods section quantifying the cooling length relative to both the viscous diffusion length and the grid scale at the adopted viscosity values, together with a brief argument that numerical diffusion cannot alter the reported inviscid-like behavior. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claim—that in the strong-cooling regime (t_cool << t_visc) the TRML behaves as effectively inviscid and preserves established scaling relations—follows directly from the outputs of the 3D viscous TRML simulations after inserting the critical viscosity scale obtained from the 2D KHI suppression runs. No step reduces a prediction or first-principles result to a fitted parameter, self-citation, or definitional equivalence; the timescale comparison and reported invariance are simulation observables, externally falsifiable, and independent of any load-bearing prior result by the same authors.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim rests on the validity of idealized hydrodynamical setups and the timescale separation between cooling and viscosity; no new particles or forces are introduced.

free parameters (1)

viscosity coefficient
Selected to bracket the critical value for KHI suppression and to span weak versus strong cooling regimes.

axioms (1)

domain assumption Idealized 2D and 3D shear-layer geometries capture the essential dynamics of astrophysical multiphase mixing layers.
Invoked when mapping 2D critical-viscosity results to 3D cooling runs.

pith-pipeline@v0.9.0 · 5834 in / 1155 out tokens · 61436 ms · 2026-05-22T17:59:09.000100+00:00 · methodology

discussion (0)

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IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

when cooling timescales are shorter than viscous timescales, key scaling relations in TRMLs remain largely intact. In this regime – which must hold for gas to remain multiphase – radiative losses dominate, and the system effectively behaves as non-viscous regardless of the actual level of viscosity.

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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