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arxiv: 2502.13444 · v1 · submitted 2025-02-19 · ⚛️ physics.flu-dyn

Impact of transverse strain on linear, transitional and self-similar turbulent mixing layers

Bradley Pascoe , Michael Groom , David L. Youngs , Ben Thornber This is my paper

Pith reviewed 2026-05-23 02:59 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords transverse strainmixing layerRayleigh-Taylor instabilityRichtmyer-Meshkov instabilitybuoyancy-drag modelturbulent mixingimplicit large eddy simulation
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The pith

Transverse compression slows turbulent mixing layer growth, predicted by rescaling drag length in buoyancy-drag model.

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

The paper examines how transverse strain modifies mixing layer evolution from Rayleigh-Taylor and Richtmyer-Meshkov instabilities when applied in planar geometry as a proxy for convergent flows. A model for the linear regime predicts amplified growth under transverse compression and matches two-dimensional simulations. In the transitional-to-turbulent regime, implicit large-eddy simulations of a multi-mode case instead show reduced growth, increased mixing, and a shift of turbulent kinetic energy toward transverse components. These turbulent changes are captured by modifying an existing buoyancy-drag model so that its drag length scale scales with the transverse expansion.

Core claim

The mixing layer width is able to be predicted by adjusting the buoyancy-drag model to utilise a drag length scale that scales with the transverse expansion. This accounts for the opposite trend to the linear regime, where turbulent growth decreases under transverse compression while the layer becomes more mixed and turbulent kinetic energy is increasingly dominated by the transverse directions.

What carries the argument

Buoyancy-drag model with drag length rescaled to follow transverse expansion of the mixing layer.

If this is right

  • Linear instability growth is amplified by transverse compression, with solutions equivalent to those in convergent geometry.
  • Turbulent mixing layer width decreases under transverse compression while the mixedness fraction increases.
  • Turbulent kinetic energy anisotropy shifts away from the unstrained self-similar state toward transverse dominance.
  • The adjusted model reproduces the observed width evolution without additional production or dissipation mechanisms.

Where Pith is reading between the lines

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

  • The mean-strain-rate framework may allow direct use of planar strain data to inform models of spherical or cylindrical convergence without separate compression-rate parameters.
  • Increased mixing under compression could alter predicted fuel-shell mix in inertial confinement fusion implosions that experience transverse strain.
  • The same drag-length rescaling could be tested against other initial perturbation spectra or against direct numerical simulations at higher Reynolds numbers.

Load-bearing premise

The effects of transverse strain on the transitional-to-turbulent regime can be captured solely by rescaling the drag length without introducing new source or sink terms for turbulent kinetic energy or mixing.

What would settle it

A three-dimensional implicit large-eddy simulation of the quarter-scale multi-mode initial condition under a fixed transverse strain rate that produces a mixing layer width differing from the rescaled buoyancy-drag prediction at late times.

Figures

Figures reproduced from arXiv: 2502.13444 by Ben Thornber, Bradley Pascoe, David L. Youngs, Michael Groom.

Figure 1
Figure 1. Figure 1: Interface at 𝜏 = 0.1 for the 2-D single-mode simulations. Heavy fluid ( 𝑓1 = 1) is red, light fluid ( 𝑓1 = 0) is blue. Major ticks indicate a distance of 𝜆(𝑡)/4, with the final wavelength marked below the plot. (a) Constant velocity, 𝑆ˆ 0 = −7.5; (b) Unstrained case; (c) Constant velocity, 𝑆ˆ 0 = 30; (d) Constant strain rate, 𝑆ˆ = −14; (e) Constant strain rate, 𝑆ˆ = 14. A second-order interpolation scheme … view at source ↗
Figure 2
Figure 2. Figure 2: Amplitude of the single mode linear regime, non-dimensionalised for the initial [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Amplitude of the single mode linear regime, non-dimensionalised by the [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Error in the amplitude for the linear regime under ( [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Contours of the volume fraction for the constant velocity ILES cases at the [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Contour of volume fraction 𝑓1 for the expansion mixing layers at Λ ≈ 1.82, bounded by 𝑓1 = 0.99 (red) and 𝑓1 = 0.01 (blue). (a) 𝑆ˆ 0 = 0.102, 𝜏 = 9.05, (b) 𝑆ˆ = 0.081, 𝜏 = 8.37, (c) 𝑆ˆ 0 = 0.025, 𝜏 = 33.5, (d) 𝑆ˆ 0 = 0.020, 𝜏 = 30.5 (a) 𝑥 𝑦 𝑧 (b) (c) (d) [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Contour of volume fraction 𝑓1 for the expansion mixing layers at Λ ≈ 0.57, bounded by 𝑓1 = 0.99 (red) and 𝑓1 = 0.01 (blue). (a) 𝑆ˆ 0 = −0.051, 𝜏 = 9.45, (b) 𝑆ˆ = −0.081, 𝜏 = 7.88, (c) 𝑆ˆ 0 = −0.013, 𝜏 = 34.9, (d) 𝑆ˆ 0 = −0.020, 𝜏 = 28.5 much closer to the unstrained simulation than was observed for cases with axial strain rates in Pascoe et al. (2024), where the strain rate causes the mixing layer to stret… view at source ↗
Figure 8
Figure 8. Figure 8: Integral width for (a) constant velocity, and (b) constant strain rate. (Zhou et al. 2016): M = ∫ 4𝜌𝑌1𝑌2𝑑𝑉 (4.4) The profiles of the mixed mass are plotted in figure 9, and show a different trend compared to the integral width. For the mixed mass, the compression cases achieve slightly higher growth and the expansion cases achieve less growth. As the name mixed mass suggests, it is not purely a measure of … view at source ↗
Figure 9
Figure 9. Figure 9: Mixed mass for (a) constant velocity and (b) constant strain rate. To reduce the impact of statistical fluctuations, the bubble and spike heights used are based off the integral measure proposed by Youngs & Thornber (2020a): ℎ¯ (𝑚) 𝑏 =       (𝑚 + 1) (𝑚 + 2) 2 ∫ 0 −∞ |𝑥 ′ | 𝑚(1 − ¯𝑓1)𝑑𝑥′ ∫ 0 −∞ (1 − ¯𝑓1)𝑑𝑥′       1/𝑚 , (4.6a) ℎ¯ (𝑚) 𝑠 = " (𝑚 + 1) (𝑚 + 2) 2 ∫ ∞ 0 |𝑥 ′ | 𝑚 ¯𝑓1𝑑𝑥′ ∫ ∞ 0 ¯𝑓1𝑑𝑥′ #1/𝑚… view at source ↗
Figure 10
Figure 10. Figure 10: Bubble and spike heights for (a) constant velocity and (b) constant strain rate. Solid lines indicate bubble height, dashed lines indicate spike height. 0 0 0 0 τ 0  0   ̂ 0  00 ̂ 0  00 ̂ 0  0000 ̂ 0   00 ̂ 0   00 (a) 0 0 0 0 τ 0  0   ̂ 00 ̂ 000 ̂ 0000 ̂  000 ̂  00 (b) [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Ratio of spike-to-bubble height for (a) constant velocity and (b) constant strain rate. molecular mixing fraction measures how well the species in the mixing layer are mixed, as measured by the volume fraction. A value of Θ = 0 suggests complete segregation, whilst Θ = 1 suggests perfect homogeneity in the plane. The molecular mixing fraction is calculated by Θ(𝑡) = ∫ 𝑓1 𝑓2𝑑𝑥 ∫ ¯𝑓1 ¯𝑓2𝑑𝑥 . (4.7) At late-t… view at source ↗
Figure 12
Figure 12. Figure 12: Mixing measures for the (a) constant velocity and (b) constant strain rate. Solid lines indicate Θ, dashed lines indicate Ψ, dotted line is FLAMENCO’s final Θ value at 𝜏 = 246 (Thornber et al. 2017). This is the same trend as observed when axial strain rates are applied to the mixing layer, such that a decrease in turbulent growth of the mixing layer corresponds to an increase in the mixedness. The differ… view at source ↗
Figure 13
Figure 13. Figure 13: Planar-averaged volume-fraction profiles for the constant velocity cases: ( [PITH_FULL_IMAGE:figures/full_fig_p030_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Planar-averaged volume-fraction profiles for the constant strain rate cases: ( [PITH_FULL_IMAGE:figures/full_fig_p030_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Total turbulent kinetic energy for (a) constant velocity and (b) constant strain rate. Solid lines indicate ILES, gray dashed lines indicate the turbulent kinetic energy model, and black dotted lines indicate the corrected turbulent kinetic energy model. 1 11 τ 1 11  ̂   1 ̂    ̂    ̂   1 ̂   1 (a) 1 11 τ 1 11  ̂  1 ̂   ̂   ̂   ̂  1 (b) [P… view at source ↗
Figure 16
Figure 16. Figure 16: Turbulent kinetic energy in the 𝑦-direction for (a) constant velocity and (b) constant strain rate. Solid lines indicate ILES, gray dashed lines indicate the turbulent kinetic energy model, and black dotted lines indicate the corrected turbulent kinetic energy model. the transverse energy and the shear production contribution whilst increasing the 𝑇𝐾 𝑋 component. By the same process, redistribution of ene… view at source ↗
Figure 17
Figure 17. Figure 17: Turbulent kinetic energy in the 𝑥-direction for (a) constant velocity and (b) constant strain rate. Solid lines indicate ILES, and black dotted lines indicate the corrected turbulent kinetic energy model. factors: 𝜀 = 𝐶𝜖 𝑇𝐾𝐸3/2 𝑊 √ 𝑀Λ2/3 (4.15) As the strain rates are only applied in two out of the three dimensions, the resulting scale is to the power of 2/3. The results for this corrected model are also … view at source ↗
Figure 18
Figure 18. Figure 18: Anisotropy of the turbulent kinetic energy for ( [PITH_FULL_IMAGE:figures/full_fig_p036_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Turbulent mass flux for (a) constant velocity, and (b) constant strain rate. Solid lines indicate results at 𝜏 = 9.843, dashed lines indicate results at 𝜏 = 34.451. 4.2.6. Enstrophy The modelling of the pressure-dilatation tensor can be avoided by analysing the vorticity or enstrophy of the flow. The vorticity is defined by the curl of the velocity field, 𝜔𝑖 = 𝜖𝑖 𝑗𝑘 𝜕𝑢𝑘 𝜕𝑥 𝑗 . (4.18) For a compressible, v… view at source ↗
Figure 20
Figure 20. Figure 20: Enstrophy in the 𝑦 − 𝑧 plane for (a) constant velocity and (b) constant strain rate. Solid lines indicate ILES, dashed lines indicate the enstrophy model. 1 11 τ 1 11 1 [PITH_FULL_IMAGE:figures/full_fig_p040_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Enstrophy in the 𝑥 − 𝑧 plane for (a) constant velocity and (b) constant strain rate. Solid lines indicate ILES, dashed lines indicate the enstrophy model. the K-L turbulence model (Dimonte & Tipton 2006) which collapses to the buoyancy-drag model under a self-similar analysis. The most relevant buoyancy-drag model to the cases investigated here are the models calibrated to the quarter-scale 𝜃-group case b… view at source ↗
Figure 22
Figure 22. Figure 22: Effective drag lengthscale as a function of non-dimensionalised integral width [PITH_FULL_IMAGE:figures/full_fig_p042_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Buoyancy-drag model for integral width: ( [PITH_FULL_IMAGE:figures/full_fig_p044_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Buoyancy-drag model for bubble height: ( [PITH_FULL_IMAGE:figures/full_fig_p044_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Buoyancy-drag model for spike height. (a) constant velocity and (b) constant strain rate. Solid lines indicate ILES results, dashed lines indicate the buoyancy-drag model [PITH_FULL_IMAGE:figures/full_fig_p044_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Convergence of constant strain rate simulations under transverse compression [PITH_FULL_IMAGE:figures/full_fig_p047_26.png] view at source ↗
read the original abstract

The growth of interfacial instabilities such as the Rayleigh-Taylor (RTI) and Richtmyer-Meshkov instability (RMI) are modified when developing in convergent geometries. Whilst these modifications are usually quantified by the compression rate and convergence rate of the mixing layer, an alternative framework is proposed, describing the evolution of the mixing layer through the effects of the mean strain rates experienced by the mixing layer. An investigation into the effect of the transverse strain rate on the mixing layer development is conducted through application of transverse strain rates in planar geometry. A model for the linear regime in planar geometry with transverse strain rate is derived, with equivalent solutions to convergent geometry, and validated with two-dimensional simulations demonstrating the amplification of the instability growth under transverse compression. The effect of the transverse strain rate on the transitional-to-turbulent mixing layer is investigated with implicit large eddy simulation based on the multi-mode quarter-scale $\theta$-group case by Thornber et al. (Phys. Fluids, vol. 29, 2017, 105107). The mixing layer's growth exhibits the opposite trend to the linear regime model, with reduced growth under transverse compression. The effect of shear-production under transverse compression causes the mixing layer to become more mixed and the turbulent kinetic energy is increasingly dominated by the transverse directions, deviating from the unstrained self-similar state. The mixing layer width is able to be predicted by adjusting the buoyancy-drag model by Youngs & Thornber (Physica D, vol. 410, 2020, 132517) to utilise a drag length scale that scales with the transverse expansion.

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 / 2 minor

Summary. The manuscript investigates the effects of transverse strain on Rayleigh-Taylor and Richtmyer-Meshkov mixing layers in planar geometry as a proxy for convergent configurations. It derives a linear stability model showing growth amplification under transverse compression (with solutions equivalent to convergent geometry), validates this with 2D simulations, and then uses implicit LES of multi-mode cases to show the opposite trend in the transitional-to-turbulent regime: reduced growth, increased mixing fraction, and TKE anisotropy with transverse dominance. The central claim is that mixing-layer width can be predicted by modifying the Youngs & Thornber buoyancy-drag model to employ a drag length scale that scales with transverse expansion.

Significance. If the adjusted buoyancy-drag model proves robust, the work supplies a strain-rate framework that could simplify modeling of convergent RTI/RMI relative to compression-rate approaches, with relevance to inertial confinement fusion and astrophysical flows. The linear-regime derivation and its 2D validation constitute a clear strength; the turbulent-regime results highlight physically interesting deviations from self-similarity.

major comments (2)
  1. [Abstract (turbulent regime) and model-adjustment section] Abstract and turbulent-regime results: the claim that mixing-layer width is predicted by rescaling the drag length in the Youngs & Thornber (Physica D, 2020) buoyancy-drag model rests on a scaling chosen to match the ILES data rather than obtained from an independent derivation or external benchmark; this renders the central turbulent prediction circular and potentially case-specific.
  2. [ILES results and model adjustment] ILES analysis: the simulations show that transverse compression increases the mixing fraction and shifts TKE dominance to the transverse components, breaking the unstrained self-similar state; the model adjustment omits any new source/sink terms for this anisotropy or enhanced production, so the width match achieved solely by drag-length rescaling does not demonstrate that the underlying turbulent-state changes have been captured.
minor comments (2)
  1. The specific functional form adopted for the transverse-expansion drag-length scaling (including any fitted coefficient) should be stated explicitly with its numerical value and the fitting procedure used.
  2. Clarify whether the linear-model derivation assumes incompressible flow or includes any compressibility corrections that would be relevant when mapping to convergent geometries.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review highlighting important aspects of our turbulent-regime analysis. We respond point-by-point to the major comments below, clarifying the physical motivation for the model adjustment while acknowledging its phenomenological nature.

read point-by-point responses

  1. Referee: [Abstract (turbulent regime) and model-adjustment section] Abstract and turbulent-regime results: the claim that mixing-layer width is predicted by rescaling the drag length in the Youngs & Thornber (Physica D, 2020) buoyancy-drag model rests on a scaling chosen to match the ILES data rather than obtained from an independent derivation or external benchmark; this renders the central turbulent prediction circular and potentially case-specific.

    Authors: The proposed scaling of the drag length with transverse expansion is guided by the strain-rate framework developed in the manuscript. The linear analysis and 2D simulations establish that transverse compression amplifies growth, while the ILES reveal the opposite trend in the turbulent regime due to strain-induced changes in mixing and anisotropy. The drag-length adjustment is therefore motivated as an effective representation of how transverse expansion alters the characteristic length in the drag term, reversing the linear trend. Although the precise functional dependence was identified to reproduce the simulated widths, it is not an arbitrary fit but a direct consequence of incorporating the transverse strain into the existing Youngs & Thornber model. We view the ILES as validation of this extension rather than the sole determinant of its form, and the approach remains testable on additional configurations. revision: no

  2. Referee: [ILES results and model adjustment] ILES analysis: the simulations show that transverse compression increases the mixing fraction and shifts TKE dominance to the transverse components, breaking the unstrained self-similar state; the model adjustment omits any new source/sink terms for this anisotropy or enhanced production, so the width match achieved solely by drag-length rescaling does not demonstrate that the underlying turbulent-state changes have been captured.

    Authors: The buoyancy-drag model is a reduced-order description whose purpose is to predict mixing-layer width, not the detailed evolution of the Reynolds-stress tensor or mixing fraction. The drag-length rescaling provides an effective means to incorporate the net influence of the observed anisotropy and altered production on the growth rate, without introducing additional transport equations. We do not claim that this adjustment resolves the internal turbulent state; it only reproduces the width evolution that results from those changes. This constitutes a limitation of the simple model, and more complete closures would be required to capture the TKE anisotropy explicitly. revision: partial

Circularity Check

2 steps flagged

Mixing layer width prediction reduces to fitted rescaling of drag length in self-cited buoyancy-drag model

specific steps
  1. fitted input called prediction [Abstract (final sentence); model-adjustment discussion]
    "The mixing layer width is able to be predicted by adjusting the buoyancy-drag model by Youngs & Thornber (Physica D, vol. 410, 2020, 132517) to utilise a drag length scale that scales with the transverse expansion."

    The scaling factor for the drag length is selected so that the model reproduces the simulated mixing-layer widths under transverse strain. The 'prediction' is therefore the output of a parameter fit to the same growth-rate data it is claimed to predict, with no independent derivation of the scaling provided.

  2. self citation load bearing [Abstract; model section]
    "adjusting the buoyancy-drag model by Youngs & Thornber (Physica D, vol. 410, 2020, 132517)"

    The load-bearing turbulent model is taken from prior work co-authored by Thornber; the only modification is the fitted drag-length rescaling. No external validation or machine-checked uniqueness result is cited to justify that this single change captures the observed TKE anisotropy and enhanced mixing.

full rationale

The linear-regime derivation is self-contained and independent. However, the central claim for the transitional-to-turbulent regime states that width is 'predicted' by adjusting the Youngs & Thornber buoyancy-drag model via a drag-length scaling chosen to match the ILES data. This adjustment is data-driven rather than derived from first principles or external benchmarks, and the base model is self-cited. The result is therefore partially forced by construction on the simulation inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work relies on standard incompressible or weakly compressible Navier-Stokes assumptions plus the specific modeling choice that transverse strain enters only through a rescaled drag length. No new particles or forces are postulated.

free parameters (1)
  • transverse-expansion drag-length scaling coefficient
    The functional dependence of the drag length on transverse strain is introduced to match the observed turbulent growth; its coefficient is not derived from first principles.
axioms (2)
  • domain assumption The mean strain-rate tensor can be imposed independently of the instability growth in planar geometry.
    Invoked when the authors apply transverse strain rates to planar mixing layers to mimic convergent geometry.
  • domain assumption The buoyancy-drag model remains structurally valid once the drag length is rescaled.
    Central modeling step for the turbulent-regime prediction.

pith-pipeline@v0.9.0 · 5833 in / 1520 out tokens · 25405 ms · 2026-05-23T02:59:57.942131+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

88 extracted references · 88 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type volume year eprint label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence ...

    work page

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

    work page

  3. [3]

    Journal of Computational Physics 181 (2), 577--616

    Allaire, Gr \'e goire , Clerc, S \'e bastien & Kokh, Samuel 2002 A Five-Equation Model for the Simulation of Interfaces between Compressible Fluids . Journal of Computational Physics 181 (2), 577--616

    work page 2002

  4. [4]

    2000 The Role of Mixing in Astrophysics

    Arnett, D. 2000 The Role of Mixing in Astrophysics . The Astrophysical Journal Supplement Series 127 (2), 213--217

    work page 2000

  5. [5]

    & Freeman, J

    Baker, L. & Freeman, J. R. 1981 Heuristic model of the nonlinear Rayleigh - Taylor instability . Journal of Applied Physics 52 (2), 655--663

    work page 1981

  6. [6]

    1951 Taylor instability on cylinders and spheres in the small amplitude approximation

    Bell, George I. 1951 Taylor instability on cylinders and spheres in the small amplitude approximation . Tech. Rep.\/ LA-1321. Los Alamos Scientific Laboratory

    work page 1951

  7. [7]

    , Harlow, F

    Besnard, D. , Harlow, F. H. , Rauenzahn, R. M. & Zemach, C. 1992 Turbulence transport equations for variable-density turbulence and their relationship to two-field models . Tech. Rep.\/ LA-12303-MS. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    work page 1992

  8. [8]

    Blaisdell, G. A. , Coleman, G. N. & Mansour, N. N. 1996 Rapid distortion theory for compressible homogeneous turbulence under isotropic mean strain . Physics of Fluids 8 (10), 2692--2705

    work page 1996

  9. [9]

    Physics of Plasmas 7 (6), 2255--2269

    Dimonte, Guy 2000 Spanwise homogeneous buoyancy-drag model for Rayleigh -- Taylor mixing and experimental evaluation . Physics of Plasmas 7 (6), 2255--2269

    work page 2000

  10. [10]

    Physics of Fluids 18 (8), 085101

    Dimonte, Guy & Tipton, Robert 2006 K- L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities . Physics of Fluids 18 (8), 085101

    work page 2006

  11. [11]

    , Flaig, M

    El Rafei, M. , Flaig, M. , Youngs, D. L. & Thornber, B. 2019 Three-dimensional simulations of turbulent mixing in spherical implosions . Physics of Fluids 31 (11), 114101

    work page 2019

  12. [12]

    & Thornber, B

    El Rafei, M. & Thornber, B. 2020 Numerical study and buoyancy--drag modeling of bubble and spike distances in three-dimensional spherical implosions . Physics of Fluids 32 (12), 124107

    work page 2020

  13. [13]

    Physical Review Fluids 9 (3), 034501

    El Rafei, Moutassem & Thornber, Ben 2024 Turbulence statistics and transport in compressible mixing driven by spherical implosions with narrowband and broadband initial perturbations . Physical Review Fluids 9 (3), 034501

    work page 2024

  14. [14]

    Physics of Plasmas 25 (6), 062126

    Elbaz, Yonatan & Shvarts, Dov 2018 Modal model mean field self-similar solutions to the asymptotic evolution of Rayleigh-Taylor and Richtmyer-Meshkov instabilities and its dependence on the initial conditions . Physics of Plasmas 25 (6), 062126

    work page 2018

  15. [15]

    2004 On the Bell -- Plesset effects: The effects of uniform compression and geometrical convergence on the classical Rayleigh -- Taylor instability

    Epstein, R. 2004 On the Bell -- Plesset effects: The effects of uniform compression and geometrical convergence on the classical Rayleigh -- Taylor instability . Physics of Plasmas 11 (11), 5114--5124

    work page 2004

  16. [16]

    Journal of Computational Physics 174 (2), 669--694

    Farhat, Charbel , Geuzaine, Philippe & Grandmont, C \'e line 2001 The Discrete Geometric Conservation Law and the Nonlinear Stability of ALE Schemes for the Solution of Flow Problems on Moving Grids . Journal of Computational Physics 174 (2), 669--694

    work page 2001

  17. [17]

    , Clark, D

    Flaig, M. , Clark, D. , Weber, C. , Youngs, D. L. & Thornber, B. 2018 Single-mode perturbation growth in an idealized spherical implosion . Journal of Computational Physics 371 , 801--819

    work page 2018

  18. [18]

    Journal of Fluid Mechanics 946 , A18

    Ge, Jin , Li, Haifeng , Zhang, Xinting & Tian, Baolin 2022 Evaluating the stretching/compression effect of Richtmyer -- Meshkov instability in convergent geometries . Journal of Fluid Mechanics 946 , A18

    work page 2022

  19. [19]

    Physics of Fluids 32 (12), 124116

    Ge, Jin , Zhang, Xin-ting , Li, Hai-feng & Tian, Bao-lin 2020 Late-time turbulent mixing induced by multimode Richtmyer -- Meshkov instability in cylindrical geometry . Physics of Fluids 32 (12), 124116

    work page 2020

  20. [20]

    Journal of Turbulence 6 , N29

    Gr \'e goire, Olivier , Souffland, Denis & Gauthier, Serge 2005 A second-order turbulence model for gaseous mixtures induced by Richtmyer --- Meshkov instability . Journal of Turbulence 6 , N29

    work page 2005

  21. [21]

    , Margolin, Len G

    Grinstein, Fenando F. , Margolin, Len G. & Rider, William . 2007 Implicit Large Eddy Simulation : Computing Turbulent Fluid Dynamics\/ . Cambridge ;: Cambridge University Press

    work page 2007

  22. [22]

    & Thornber, B

    Groom, M. & Thornber, B. 2020 The influence of initial perturbation power spectra on the growth of a turbulent mixing layer induced by Richtmyer -- Meshkov instability . Physica D: Nonlinear Phenomena 407 , 132463

    work page 2020

  23. [23]

    Journal of Fluid Mechanics 964 , A21

    Groom, Michael & Thornber, Ben 2023 Numerical simulation of an idealised Richtmyer -- Meshkov instability shock tube experiment . Journal of Fluid Mechanics 964 , A21

    work page 2023

  24. [24]

    Hansom, J. C. V. , Rosen, P. A. , Goldack, T. J. , Oades, K. , Fieldhouse, P. , Cowperthwaite, N. , Youngs, D. L. , Mawhinney, N. & Baxter, A. J. 1990 Radiation driven planar foil instability and mix experiments at the AWE HELEN laser* . Laser and Particle Beams 8 (1-2), 51--71

    work page 1990

  25. [25]

    Hunt, J. C. R. & Carruthers, D. J. 1990 Rapid distortion theory and the `problems' of turbulence . Journal of Fluid Mechanics 212 , 497--532

    work page 1990

  26. [26]

    Proceedings of the Royal Society of London

    Jeans, James Hopwood 1997 The propagation of earthquake waves . Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 102 (718), 554--574

    work page 1997

  27. [27]

    Joggerst, C. C. , Nelson, Anthony , Woodward, Paul , Lovekin, Catherine , Masser, Thomas , Fryer, Chris L. , Ramaprabhu, P. , Francois, Marianne & Rockefeller, Gabriel 2014 Cross-code comparisons of mixing during the implosion of dense cylindrical and spherical shells . Journal of Computational Physics 275 , 154--173

    work page 2014

  28. [28]

    A 1990 Enstrophy budget in decaying compressible turbulence

    Kida, S & Orszag, S. A 1990 Enstrophy budget in decaying compressible turbulence . Journal of scientific computing 5 (1), 1--34

    work page 1990

  29. [29]

    Journal of Computational Physics 208 (2), 570--615

    Kim, Kyu Hong & Kim, Chongam 2005 Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows: Part II : Multi-dimensional limiting process . Journal of Computational Physics 208 (2), 570--615

    work page 2005

  30. [30]

    In Simulation and Modeling of Turbulent Flows \/ (ed

    Launder, Brian E 1996 An Introduction to Single-Point Closure Methodology . In Simulation and Modeling of Turbulent Flows \/ (ed. Thomas B Gatski, M Yousuff Hussaini & John L Lumley ) , p. 0 . Oxford University Press

    work page 1996

  31. [31]

    Launder, B. E. , Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure . Journal of Fluid Mechanics 68 (3), 537--566

    work page 1975

  32. [32]

    The Astrophysical Journal 122 , 1

    Layzer, David 1955 On the Instability of Superposed Fluids in a Gravitational Field . The Astrophysical Journal 122 , 1

    work page 1955

  33. [33]

    Physics of Fluids 31 (5), 054102

    Li, Haifeng , He, Zhiwei , Zhang, Yousheng & Tian, Baolin 2019 On the role of rarefaction/compression waves in Richtmyer-Meshkov instability with reshock . Physics of Fluids 31 (5), 054102

    work page 2019

  34. [34]

    Physical Review E 103 (5), 053109

    Li, Haifeng , Tian, Baolin , He, Zhiwei & Zhang, Yousheng 2021 a\/ Growth mechanism of interfacial fluid-mixing width induced by successive nonlinear wave interactions . Physical Review E 103 (5), 053109

    work page 2021

  35. [35]

    Journal of Fluid Mechanics 901 , A38

    Li, Ming , Ding, Juchun , Zhai, Zhigang , Si, Ting , Liu, Naian , Huang, Shenghong & Luo, Xisheng 2020 On divergent Richtmyer -- Meshkov instability of a light/heavy interface . Journal of Fluid Mechanics 901 , A38

    work page 2020

  36. [36]

    Journal of Fluid Mechanics 928

    Li, Xinliang , Fu, Yaowei , Yu, Changping & Li, Li 2021 b\/ Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer -- Meshkov instabilities . Journal of Fluid Mechanics 928

    work page 2021

  37. [37]

    Physics of Plasmas 21 (2), 020501

    Lindl, John , Landen, Otto , Edwards, John , Moses, Ed & NIC Team 2014 Review of the National Ignition Campaign 2009-2012 . Physics of Plasmas 21 (2), 020501

    work page 2014

  38. [38]

    , Amendt, Peter , Berger, Richard L

    Lindl, John D. , Amendt, Peter , Berger, Richard L. , Glendinning, S. Gail , Glenzer, Siegfried H. , Haan, Steven W. , Kauffman, Robert L. , Landen, Otto L. & Suter, Laurence J. 2004 The physics basis for ignition using indirect-drive targets on the National Ignition Facility . Physics of Plasmas 11 (2), 339--491

    work page 2004

  39. [39]

    , Pullin, D

    Lombardini, M. , Pullin, D. I. & Meiron, D. I. 2014 a\/ Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth . Journal of Fluid Mechanics 748 , 85--112

    work page 2014

  40. [40]

    , Pullin, D

    Lombardini, M. , Pullin, D. I. & Meiron, D. I. 2014 b\/ Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics . Journal of Fluid Mechanics 748 , 113--142

    work page 2014

  41. [41]

    Journal of Computational Physics 194 (1), 304--328

    Luo, Hong , Baum, Joseph D & L \"o hner, Rainald 2004 On the computation of multi-material flows using ALE formulation . Journal of Computational Physics 194 (1), 304--328

    work page 2004

  42. [42]

    Journal of Fluid Mechanics 877 , 130--141

    Luo, Xisheng , Li, Ming , Ding, Juchun , Zhai, Zhigang & Si, Ting 2019 Nonlinear behaviour of convergent Richtmyer -- Meshkov instability . Journal of Fluid Mechanics 877 , 130--141

    work page 2019

  43. [43]

    Marshall, J. S. & Grant, J. R. 1994 Evolution and breakup of vortex rings in straining and shearing flows . Journal of Fluid Mechanics 273 , 285--312

    work page 1994

  44. [44]

    , Saurel, R

    Massoni, J. , Saurel, R. , Nkonga, B. & Abgrall, R. 2002 Proposition de m \'e thodes et mod \`e les eul \'e riens pour les probl \`e mes \`a interfaces entre fluides compressibles en pr \'e sence de transfert de chaleur: Some models and Eulerian methods for interface problems between compressible fluids with heat transfer . International Journal of Heat a...

    work page 2002

  45. [45]

    Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave . Fluid Dynamics 4 (5), 101--104

    work page 1969

  46. [46]

    Miles, A. R. 2004 Bubble merger model for the nonlinear Rayleigh -- Taylor instability driven by a strong blast wave . Physics of Plasmas 11 (11), 5140--5155

    work page 2004

  47. [47]

    2009 The Blast-Wave-Driven Instability as a Vehicle for Understanding Supernova Explosion Structure

    Miles, Aaron R. 2009 The Blast-Wave-Driven Instability as a Vehicle for Understanding Supernova Explosion Structure . The Astrophysical Journal 696 , 498--514

    work page 2009

  48. [48]

    , Shavit, A

    Naot, D. , Shavit, A. & Wolfshtein, M. 1970 Interactions between components of the turbulent velocity tensor correlation due to pressure fluctuations . Israel J. Technol 8 , 259--269

    work page 1970

  49. [49]

    , Arazi, L

    Oron, D. , Arazi, L. , Kartoon, D. , Rikanati, A. , Alon, U. & Shvarts, D. 2001 Dimensionality dependence of the Rayleigh -- Taylor and Richtmyer -- Meshkov instability late-time scaling laws . Physics of Plasmas 8 (6), 2883--2889

    work page 2001

  50. [50]

    , Groom, M

    Pascoe, B. , Groom, M. , Youngs, D.L. & Thornber, B. 2024 Modelling the effects of the R ichtmyer- M eshkov instability under axial strain . (submitted)

    work page 2024

  51. [51]

    & Price, A.T

    Penney, W.G. & Price, A.T. 1942 On the changing form of a nearly spherical submarine bubble . Underwarter Explosion Research 2 , 145--161

    work page 1942

  52. [52]

    Plesset, M. S. 1954 On the Stability of Fluid Flows with Spherical Symmetry . Journal of Applied Physics 25 (1), 96--98

    work page 1954

  53. [53]

    , Jones, T

    Porter, David H. , Jones, T. W. & Ryu, Dongsu 2015 VORTICITY , SHOCKS , AND MAGNETIC FIELDS IN SUBSONIC , ICM-LIKE TURBULENCE . The Astrophysical Journal 810 (2), 93

    work page 2015

  54. [54]

    1998 Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration

    Ramshaw, John D. 1998 Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration . Physical Review E 58 (5), 5834--5840

    work page 1998

  55. [55]

    Proceedings of the London Mathematical Society s1-14 (1), 170--177

    Rayleigh 1882 Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density . Proceedings of the London Mathematical Society s1-14 (1), 170--177

    work page

  56. [56]

    1960 Taylor instability in shock acceleration of compressible fluids

    Richtmyer, Robert D. 1960 Taylor instability in shock acceleration of compressible fluids . Communications on Pure and Applied Mathematics 13 (2), 297--319

    work page 1960

  57. [57]

    Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence . Tech. Rep.\/ NASA-TM-81315. NASA

    work page 1981

  58. [58]

    1951 Statistische Theorie nichthomogener Turbulenz

    Rotta, J. 1951 Statistische Theorie nichthomogener Turbulenz . Zeitschrift fur Physik 129 , 547--572

    work page 1951

  59. [59]

    1992 The pressure--dilatation correlation in compressible flows

    Sarkar, S. 1992 The pressure--dilatation correlation in compressible flows . Physics of Fluids A: Fluid Dynamics 4 (12), 2674--2682

    work page 1992

  60. [60]

    , Livescu, Daniel , Gore, Robert A

    Schwarzkopf, John D. , Livescu, Daniel , Gore, Robert A. , Rauenzahn, Rick M. & Ristorcelli, J. Raymond 2011 Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids . Journal of Turbulence 12 , N49

    work page 2011

  61. [61]

    Physical Review Fluids 7 (1), 014605

    Soulard, Olivier & Griffond, J \'e r \^o me 2022 Permanence of large eddies in Richtmyer--Meshkov turbulence for weak shocks and high Atwood numbers . Physical Review Fluids 7 (1), 014605

    work page 2022

  62. [62]

    & Ruuth, Steven J

    Spiteri, Raymond J. & Ruuth, Steven J. 2002 A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods . SIAM Journal on Numerical Analysis 40 (2), 469--491

    work page 2002

  63. [63]

    Taylor, Geoffrey Ingram 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I . Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 201 (1065), 192--196

    work page 1950

  64. [64]

    Thomas, P. D. & Lombard, C. K. 1979 Geometric Conservation Law and Its Application to Flow Computations on Moving Grids . AIAA Journal 17 (10), 1030--1037

    work page 1979

  65. [65]

    , Drikakis, D

    Thornber, B. , Drikakis, D. , Williams, R. J. R. & Youngs, D. 2008 a\/ On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes . Journal of Computational Physics 227 (10), 4853--4872

    work page 2008

  66. [66]

    , Drikakis, D

    Thornber, B. , Drikakis, D. , Youngs, D. L. & Williams, R. J. R. 2010 The influence of initial conditions on turbulent mixing due to Richtmyer -- Meshkov instability . Journal of Fluid Mechanics 654 , 99--139

    work page 2010

  67. [67]

    , Griffond, J

    Thornber, B. , Griffond, J. , Bigdelou, P. , Boureima, I. , Ramaprabhu, P. , Schilling, O. & Williams, R. J. R. 2019 Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability . Physics of Fluids 31 (9), 096105

    work page 2019

  68. [68]

    , Griffond, J

    Thornber, B. , Griffond, J. , Poujade, O. , Attal, N. , Varshochi, H. , Bigdelou, P. , Ramaprabhu, P. , Olson, B. , Greenough, J. , Zhou, Y. , Schilling, O. , Garside, K. A. , Williams, R. J. R. , Batha, C. A. , Kuchugov, P. A. , Ladonkina, M. E. , Tishkin, V. F. , Zmitrenko, N. V. , Rozanov, V. B. & Youngs, D. L. 2017 Late-time growth rate, mixing, and a...

    work page 2017

  69. [69]

    Journal of Computational Physics 372 , 256--280

    Thornber, Ben , Groom, Michael & Youngs, David 2018 A five-equation model for the simulation of miscible and viscous compressible fluids . Journal of Computational Physics 372 , 256--280

    work page 2018

  70. [70]

    , Mosedale, A

    Thornber, B. , Mosedale, A. , Drikakis, D. , Youngs, D. & Williams, R. J. R. 2008 b\/ An improved reconstruction method for compressible flows with low Mach number features . Journal of Computational Physics 227 (10), 4873--4894

    work page 2008

  71. [71]

    Toro, E. F. , Spruce, M. & Speares, W. 1994 Restoration of the contact surface in the HLL-Riemann solver . Shock Waves 4 (1), 25--34

    work page 1994

  72. [72]

    Physical Review Fluids 3 (1), 014001

    Vandenboomgaerde, Marc , Rouzier, Pascal , Souffland, Denis , Biamino, Laurent , Jourdan, Georges , Houas, Lazhar & Mariani, Christian 2018 Nonlinear growth of the converging Richtmyer-Meshkov instability in a conventional shock tube . Physical Review Fluids 3 (1), 014001

    work page 2018

  73. [73]

    & Thornber, B

    Walchli, B. & Thornber, B. 2017 Reynolds number effects on the single-mode Richtmyer-Meshkov instability . Physical Review E 95 (1), 013104

    work page 2017

  74. [74]

    Wang, L. F. , Wu, J. F. , Guo, H. Y. , Ye, W. H. , Liu, Jie , Zhang, W. Y. & He, X. T. 2015 Weakly nonlinear Bell-Plesset effects for a uniformly converging cylinder . Physics of Plasmas 22 (8), 082702

    work page 2015

  75. [75]

    Journal of Turbulence 24 (9-10), 419--444

    Wang, Tao , Zhong, Min , Wang, Bing , Li, Ping & Bai, Jingsong 2023 Evolution of turbulent mixing driven by implosion in spherical geometry . Journal of Turbulence 24 (9-10), 419--444

    work page 2023

  76. [76]

    & Meschede, Matthias 2018 SHTools : Tools for Working with Spherical Harmonics

    Wieczorek, Mark A. & Meschede, Matthias 2018 SHTools : Tools for Working with Spherical Harmonics . Geochemistry, Geophysics, Geosystems 19 (8), 2574--2592

    work page 2018

  77. [77]

    , Jayayaraj, J

    Woodward, Paul R. , Jayayaraj, J. , Lin, p-H. , Knox, Mike , Porter, David H. , Fryer, Christopher L. , Dimonte, Guy , Joggerst, Candace C. , Rockefeller, Gabriel M. , Dai, William W. , Kares, Robert J. & Thomas, Vincent A. 2013 Simulating Turbulent Mixing from Richtmyer-Meshkov and Rayleigh-Taylor Instabilities in Converging Geometries using Moving Carte...

    work page 2013

  78. [78]

    Advances in Mechanical Engineering 6 , 614189

    Yang, Qingchun , Chang, Juntao & Bao, Wen 2014 Richtmyer- Meshkov Instability Induced Mixing Enhancement in the Scramjet Combustor with a Central Strut . Advances in Mechanical Engineering 6 , 614189

    work page 2014

  79. [79]

    & Thornber, Ben 2020 a\/ Buoyancy-- Drag modelling of bubble and spike distances for single-shock Richtmyer -- Meshkov mixing

    Youngs, David L. & Thornber, Ben 2020 a\/ Buoyancy-- Drag modelling of bubble and spike distances for single-shock Richtmyer -- Meshkov mixing . Physica D: Nonlinear Phenomena 410 , 132517

    work page 2020

  80. [80]

    & Thornber, Ben 2020 b\/ Early Time Modifications to the Buoyancy-Drag Model for Richtmyer -- Meshkov Mixing

    Youngs, David L. & Thornber, Ben 2020 b\/ Early Time Modifications to the Buoyancy-Drag Model for Richtmyer -- Meshkov Mixing . Journal of Fluids Engineering 142 (121107)

    work page 2020

Showing first 80 references.