Aglitskiy, Y., Velikovich, A. L., Karasik, M., Metzler, N., Zalesak, S. T., Schmitt, A. J., Phillips, L., Gardner, J. H., Serlin, V., Weaver, J. L. & Obenschain, S. P.
2010
Basic hydrodynamics of Richtmyer–Meshkov-type growth and oscillations in the inertial confinement fusion-relevant conditions. Phil. Trans. R. Soc. Lond. A
368 (1916), 1739–1768.

Almgren, A. S., Bell, J. B., Rendleman, C. A. & Zingale, M.
2006
Low Mach number modeling of type Ia supernovae I. Hydrodynamics. Astrophys. J.
637, 922–936.

Arnett, D.
2000
The role of mixing in astrophysics. Astrophys. J. Suppl.
127, 213–217.

Arnett, W. D., Bahcall, J. N., Kirshner, R. P. & Stanford, E. W.
1989
Supernova 1987a. Annu. Rev. Astron. Astrophys.
27, 629–700.

Balakumar, B. J., Orlicz, G. C., Ristorcelli, J. R., Balasubramanian, S., Prestridge, K. P. & Tomkins, C. D.
2012
Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics. J. Fluid Mech.
696, 67–93.

Balasubramanian, S., Orlicz, G. C. & Prestridge, K. P.
2013
Experimental study of initial condition dependence on turbulent mixing in shock-accelerated Richtmyer–Meshkov fluid layers. J. Turbul.
14 (3), 170–196.

Balasubramanian, S., Orlicz, G. C., Prestridge, K. P. & Balakumar, B. J.
2012
Experimental study of initial condition dependence on Richtmyer–Meshkov instability in the presence of reshock. Phys. Fluids
24, 034103.

Batchelor, G. K. & Proudman, I.
1956
The large-scale structure of homogeneous turbulence. Phil. Trans. R. Soc. Lond. A
248, 369–405.

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. *Recon Tech. Rep.* No. 92, 33159. NASA STI.

Brouillette, M.
2002
The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech.
34, 445–468.

Cabot, W. H. & Cook, A. W.
2006
Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae. Nat. Phys.
2 (8), 562–568.

Chapman, S. & Cowling, T. G.
1990
The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity. Cambridge University Press.

Cohen, R. H., Dannevik, W. P., Dimits, A. M., Eliason, D. E., Mirin, A. A., Zhou, Y., Porter, D. H. & Woodward, P. R.
2002
Three-dimensional simulation of a Richtmyer–Meshkov instability with a two-scale initial perturbation. Phys. Fluids
14 (10), 3692–3709.

Cook, A. W.
2007
Artificial fluid properties for large-eddy simulation of compressible turbulent mixing. Phys. Fluids
19 (5), 055103.

Cook, A. W.
2009
Enthalpy diffusion in multicomponent flows. Phys. Fluids
21, 055109.

Cook, A. W., Cabot, W. & Miller, P. L.
2004
The mixing transition in Rayleigh–Taylor instability. J. Fluid Mech.
511, 333–362.

Dimonte, G., Frerking, C. E. & Schneider, M.
1995
Richtmyer–Meshkov instability in the turbulent regime. Phys. Rev. Lett.
74, 4855–4858.

Dimonte, G. & Schneider, M.
2000
Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories. Phys. Fluids
12 (2), 304–321.

Dimotakis, P. E.
2000
The mixing transition in turbulent flows. J. Fluid Mech.
409, 69–98.

Drikakis, D.
2003
Advances in turbulent flow computations using high-resolution methods. Prog. Aerosp. Sci.
39 (6–7), 405–424.

Drikakis, D., Hahn, M., Mosedale, A. & Thornber, B.
2009
Large eddy simulation using high-resolution and high-order methods. Phil. Trans. R. Soc. Lond. A
367 (1899), 2985–2997.

Fedkiw, R. P., Merriman, B. & Osher, S.
1997
High accuracy numerical methods for thermally perfect gas flows with chemistry. J. Comput. Phys.
190, 175–190.

Gottlieb, S. & Shu, C.-W.
1998
Total variation diminishing Runge–Kutta schemes. Math. Comput.
67, 73.

Grinstein, F. F., Gowardhan, A. A. & Wachtor, A. J.
2011
Simulations of Richtmyer–Meshkov instabilities in planar shock-tube experiments. Phys. Fluids
23, 034106.

Hahn, M., Drikakis, D., Youngs, D. L. & Williams, R. J. R.
2011
Richtmyer–Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow. Phys. Fluids
23 (4), 046101.

Hill, D. J., Pantano, C. & Pullin, D. I.
2006
Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock. J. Fluid Mech.
557, 29–61.

Hill, D. J. & Pullin, D. I.
2004
Hybrid tuned center-difference-WENO method for large eddy simulations in the presence of strong shocks. J. Comput. Phys.
194, 435–450.

Hu, X. Y. & Adams, N. A.
2011
Scale separation for implicit large eddy simulation. J. Comput. Phys.
230 (19), 7240–7249.

Hu, X. Y., Adams, N. A. & Shu, C.-W.
2013
Positivity-preserving method for high-order conservative schemes solving compressible Euler equations. J. Comput. Phys.
242, 169–180.

Hu, X. Y., Wang, Q. & Adams, N. A.
2010
An adaptive central-upwind weighted essentially non-oscillatory scheme. J. Comput. Phys.
229 (23), 8952–8965.

Ishida, T., Davidson, P. A. & Kaneda, Y.
2006
On the decay of isotropic turbulence. J. Fluid Mech.
564, 455–475.

Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S.
1993
The structure of intense vorticity in isotropic turbulence. J. Fluid Mech.
255, 65–90.

Kennedy, C. A., Carpenter, M. H. & Lewis, M. R.
2000
Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations. Appl. Numer. Maths
35 (3), 177–219.

Khokhlov, A. M., Oran, E. S. & Thomas, G. O.
1999
Numerical simulation of deflagration-to-detonation transition: the role of shock–flame interactions in turbulent flames. Combust. Flame
117 (1–2), 323–339.

Kolmogorov, A. N.
1941
On the degeneration of isotropic turbulence in an incompressible viscous fluid. Dokl. Akad. Nauk SSSR
31, 538–541.

Kosović, B., Pullin, D. I. & Samtaney, R.
2002
Subgrid-scale modeling for large-eddy simulations of compressible turbulence. Phys. Fluids
14 (4), 1511–1522.

Larouturou, B. & Fezoui, L.
1989
On the equations of multi-component perfect or real gas inviscid flow. In Nonlinear Hyperbolic Problems, Lecture Notes in Mathematics, vol. 1402, pp. 69–97. Springer.

Lele, S. K.
1992
Compact finite-difference schemes with spectral-like resolution. J. Comput. Phys.
103, 16–42.

Lindl, J. D., McCrory, R. L. & Campbell, E. M.
1992
Progress toward ignition and burn propagation in inertial confinement fusion. Phys. Today
45 (9), 32–40.

Lombardini, M., Hill, D. J., Pullin, D. I. & Meiron, D. I.
2011
Atwood ratio dependence of Richtmyer–Meshkov flows under reshock conditions using large-eddy simulations. J. Fluid Mech.
670, 439–480.

Lombardini, M., Pullin, D. I. & Meiron, D. I.
2012
Transition to turbulence in shock-driven mixing: a Mach number study. J. Fluid Mech.
690, 203–226.

Mani, A., Larsson, J. & Moin, P.
2009
Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks. J. Comput. Phys.
228 (19), 7368–7374.

Meshkov, E. E.
1969
Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn.
4, 151–157.

Mikaelian, K. O.
1989
Turbulent mixing generated by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Physica D
36 (3), 343–357.

Olson, B. J. & Cook, A. W.
2007
Rayleigh–Taylor shock waves. Phys. Fluids
19, 128108.

Olson, B. J., Larsson, J., Lele, S. K. & Cook, A. W.
2011
Non-linear effects in the combined Rayleigh–Taylor/Kelvin–Helmholtz instability. Phys. Fluids
23, 114107.

Orlicz, G. C., Balasubramanian, S. & Prestridge, K. P.
2013
Incident shock Mach number effects on Richtmyer–Meshkov mixing in a heavy gas layer. Phys. Fluids
25 (11), 114101.

Pullin, D. I.
2000
A vortex-based model for the subgrid flux of a passive scalar. Phys. Fluids
12 (9), 2311–2319.

Ramshaw, J. D.
1990
Self-consistent effective binary diffusion in multicomponent gas mixtures. J. Non-Equilib. Thermodyn.
15, 295–300.

Rayleigh, Lord
1883
Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc.
14, 170–177.

Reid, R. C., Pransuitz, J. M. & Poling, B. E.
1987
The Properties of Gases and Liquids. McGraw-Hill.

Richtmyer, R. D.
1960
Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths
13, 297–319.

Roe, P. L.
1981
Approximate Riemann solvers, parameter and difference schemes. J. Comput. Phys.
43, 357–372.

Saffman, P. G.
1967a
Note on decay of homogeneous turbulence. Phys. Fluids
10, 1349.

Saffman, P. G.
1967b
The large-scale structure of homogeneous turbulence. J. Fluid Mech.
27, 581–593.

Schilling, O. & Latini, M.
2010
High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data. Acta Math. Sci.
30B, 595–620.

Schilling, O., Latini, M. & Don, W. S.
2007
Physics of reshock and mixing in single-mode Richtmyer–Meshkov instability. Phys. Rev. E
76, 026319.

Taccetti, J. M., Batha, S. H., Fincke, J. R., Delamater, N. D., Lanier, N. E., Magelssen, G. R., Hueckstaedt, R. M., Rothman, S. D., Horsfield, C. J. & Parker, K. W.
2005
Richtmyer–Meshkov instability reshock experiments using laser-driven double-cylinder implosions. In High Energy Density Laboratory Astrophysics (ed. Kyrala, G. A.), pp. 327–331. Springer.

Taylor, G.
1950
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Part 1. Waves on fluid sheets. Proc. R. Soc. Lond. A
201, 192–196.

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. J. Fluid Mech.
654, 99–139.

Thornber, B., Drikakis, D., Youngs, D. L. & Williams, R. J. R.
2011
Growth of a Richtmyer–Meshkov turbulent layer after reshock. Phys. Fluids
23, 095107.

Thornber, B., Drikakis, D., Youngs, D. L. & Williams, R. J. R.
2012
Physics of the single-shocked and reshocked Richtmyer–Meshkov instability. J. Turbul.
13 (1), N10.

Thornber, B., Mosedale, A., Drikakis, D., Youngs, D. & Williams, R. J. R.
2008
An improved reconstruction method for compressible flows with low Mach number features. J. Comput. Phys.
227 (10), 4873–4894.

Tomkins, C. D., Balakumar, B. J., Orlicz, G., Prestridge, K. P. & Ristorcelli, J. R.
2013
Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence. J. Fluid Mech.
735, 288–306.

Toro, E. F.
1999
Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer.

Tritschler, V. K., Avdonin, A., Hickel, S., Hu, X. Y. & Adams, N. A.
2014
Quantification of initial-data uncertainty on a shock-accelerated gas cylinder. Phys. Fluids
26 (2), 026101.

Tritschler, V. K., Hickel, S., Hu, X. Y. & Adams, N. A.
2013a
On the Kolmogorov inertial subrange developing from Richtmyer–Meshkov instability. Phys. Fluids
25, 071701.

Tritschler, V. K., Hu, X. Y., Hickel, S. & Adams, N. A.
2013b
Numerical simulation of a Richtmyer–Meshkov instability with an adaptive central-upwind 6th-order WENO scheme. Phys. Scr.
T155, 014016.

Weber, C. R., Cook, A. W. & Bonazza, R.
2013
Growth rate of a shocked mixing layer with known initial perturbations. J. Fluid Mech.
725, 372–401.

Weber, C., Haehn, N., Oakley, J., Rothamer, D. & Bonazza, R.
2012
Turbulent mixing measurements in the Richtmyer–Meshkov instability. Phys. Fluids
24, 074105.

Weber, C. R., Haehn, N. S., Oakley, J. G., Rothamer, D. A. & Bonazza, R.
2014
An experimental investigation of the turbulent mixing transition in the Richtmyer–Meshkov instability. J. Fluid Mech.
748, 457–487.

Wilczek, M., Daitche, A. & Friedrich, R.
2011
On the velocity distribution in homogeneous isotropic turbulence: correlations and deviations from gaussianity. J. Fluid Mech.
676, 191–217.

Yang, J., Kubota, T. & Zukoski, E. E.
1993
Applications of shock-induced mixing to supersonic combustion. AIAA J.
31, 854–862.

Youngs, D. L.
1991
Three-dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Phys. Fluids A: Fluid Dyn.
3 (5), 1312–1320.

Youngs, D. L.
1994
Numerical simulations of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Laser Part. Beams
12 (2), 538–544.

Youngs, D. L.2004 Effect of initial conditions on self-similar turbulent mixing. In *Proceedings of the International Workshop on the Physics of Compressible Turbulent Mixing*, vol. 9.

Youngs, D. L.
2007
Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics, pp. 392–412. Cambridge University Press.

Zabusky, N. J.
1999
Vortex paradigm for accelerated inhomogeneous flows: visiometrics for the Rayleigh–Taylor and Richtmyer–Meshkov environments. Annu. Rev. Fluid Mech.
31, 495–536.

Zhou, Y.
2001
A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Fluids
13 (2), 538–543.