Abramowitz, M. & Stegun, I. A.
1964 *Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables*. National Bureau of Standards Applied Mathematics Series.

Aure, R. & Jacobs, J. W
2008
Particle image velocimetry study of the shock-induced single mode Richtmyer–Meshkov instability. Shock Waves
18, 161–167.

Badcock, K. J.
1992
A numerical simulation of boundary layer effects in a shock tube. Intl J. Numer. Meth. Fluids
14, 1151–1171.

Balakumar, B. J., Orlicz, G. C., Tomkins, C. D. & Prestridge, K. P.
2008
Dependence of growth patterns and mixing width on initial conditions in Richtmyer–Meshkov unstable fluid layers. Phys. Scr.
T123, 014013.

Benjamin, R. F., Trease, H. E. & Shaner, J. W.
1984
Coherent density gradients in water compressed by a modulated shock wave. Phys. Fluids
27, 2390–2393.

Bonazza, R. & Sturtevant, B.
1996
X-ray measurements of growth rates at a gas interface accelerated by shock waves. Phys. Fluids
8, 2496–2512.

Brocher, E. F.
1964
Hot flow length and testing time in real shock tube flow. Phys. Fluids
7, 347–351.

Collins, B. D. & Jacobs, J. W.
2002
PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/
${\mathrm{SF} }_{6} $
interface. J. Fluid Mech.
464, 113–136.
Cook, A. W.
2007
Artificial fluid properties for large-eddy simulation of compressible turbulent mixing. Phys. Fluids
19, 055103.

Cook, A. W. & Cabot, W. H.
2004
A high-wavenumber viscosity for high-resolution numerical methods. J. Comput. Phys.
195, 594–601.

Cook, A. W. & Cabot, W. H.
2005
Hyperviscosity for shock–turbulence interactions. J. Comput. Phys.
203, 379–385.

Dimonte, G. & Ramaprabhu, P.
2010
Simulations and model of the nonlinear Richtmyer–Meshkov instability. Phys. Fluids
22, 4014104.

Edwards, M. J., Lindl, J. D., Spears, B. K., Weber, S. V., Atherton, L. J., Bleuel, D. L., Bradley, D. K., Callahan, D. A., Cerjan, C. J., Clark, D., Collins, G. W., Fair, J. E., Fortner, R. J., Glenzer, S. H., Haan, S. W., Hammel, B. A., Hamza, A. V., Hatchett, S. P., Izumi, N., Jacoby, B., Jones, O. S., Koch, J. A., Kozioziemski, B. J., Landen, O. L., Lerche, R., MacGowan, B. J., MacKinnon, A. J., Mapoles, E. R., Marinak, M. M., Moran, M., Moses, E. I., Munro, D. H., Schneider, D. H., Sepke, S. M., Shaughnessy, D. A., Springer, P. T., Tommasini, R., Bernstein, L., Stoeffl, W., Betti, R., Boehly, T. R., Sangster, T. C., Glebov, V. Y., McKenty, P. W., Regan, S. P., Edgell, D. H., Knauer, J. P., Stoeckl, C., Harding, D. R., Batha, S., Grim, G., Herrmann, H. W., Kyrala, G., Wilke, M., Wilson, D. C., Frenje, J., Petrasso, R., Moreno, K., Huang, H., Chen, K. C., Giraldez, E., Kilkenny, J. D., Mauldin, M., Hein, N., Hoppe, M., Nikroo, A. & Leeper, R. J.
2011
The experimental plan for cryogenic layered target implosions on the national ignition facility: the inertial confinement approach to fusion. Phys. Plasmas
18
(5), 051003.

Glass, I. I. & Patterson, G. N.
1955
A theoretical and experimental study of shock-tube flows. J. Aero. Sci.
22, 73–100.

Goncharov, V. N.
2002
Analytical model of nonlinear, single-mode, classical Rayleigh–Taylor instability at arbitrary Atwood numbers. Phys. Rev. Lett.
88, 134502.

Grinstein, F. F., Gowhardhan, 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, 046101.

Herrmann, M., Moin, P. & Abarzhi, S. I.
2008
Nonlinear evolution of the Richtmyer–Meshkov instability. J. Fluid Mech.
612, 311–338.

Holmes, R. L., Dimonte, G., Fryxell, B., Gittings, M. L., Grove, J. W., Schneider, M., Sharp, D. H., Velikovich, A. L., Weaver, R. P. & Zhang, Q.
1999
Richtmyer–Meshkov instability growth: experiment, simulation and theory. J. Fluid Mech.
389, 55–79.

Huerte Ruiz de Lira, C., Velikovich, A. L. & Wouchuk, J. G.
2011
Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic density field. Phys. Rev. E
83, 056320.

Jacobs, J. W.
1993
The dynamics of shock accelerated light and heavy gas cylinders. Phys. Fluids A
5, 2239–2247.

Jacobs, J. W., Jenkins, D. G., Klein, D. L. & Benjamin, R. F.
1995
Nonlinear growth of the shock-accelerated instability of a thin fluid layer. J. Fluid Mech.
295, 23–42.

Jacobs, J. W., Klein, D. L., Jenkins, D. G. & Benjamin, R. F.
1993
Instability growth patterns of a shock-accelerated thin fluid layer. Phys. Rev. Lett.
70, 583–586.

Jacobs, J. W. & Krivets, V. V.
2005
Experiments on the late-time development of single-mode Richtmyer–Meshkov instability. Phys. Fluids
17, 034105.

Jacobs, J. W. & Sheeley, J. M.
1996
Experimental study of the Richtmyer–Meshkov instability of incompressible fluids. Phys. Fluids
8, 405–415.

Jones, M. A. & Jacobs, J. W.
1997
A membraneless experiment for the study of Richtmyer–Meshkov instability of a shock-accelerated gas interface. Phys. Fluids
9, 3078–3085.

Keane, R. D. & Adrian, R. J.
1990
Optimization of particle image velocimeters. Part 1. Double pulsed systems. Meas. Sci. Technol.
1, 1202–1215.

Keane, R. D. & Adrian, R. J.
1991
Optimization of particle image velocimeters. Part 2. Multiple pulsed systems. Meas. Sci. Technol.
2, 963–974.

Kifonidis, K., Plewa, T., Sheck, L., Janka, H.-T. & Müller, E.
2006
Non-spherical core collapse supernovae. Astron. Astrophys.
453, 661–678.

Kolev, T. V. & Rieben, R. N.
2009
A tensor artificial viscosity using finite element approach. J. Comput. Phys.
228, 8336–8366.

Krechetnikov, R.
2009
Rayleigh–Taylor and Richtmyer–Meshkov instabilities of flat and curved interfaces. J. Fluid. Mech.
625, 387–410.

Layzer, D.
1955
On the instability of superposed fluids in a gravitational field. Astrophys. Rev. J.
122, 1–12.

Likhachev, O. A. & Jacobs, J. W.
2005
A vortex model for Richtmyer–Meshkov instability accounting for finite Atwood number. Phys. Fluids
17, 031704.

Liu, B. Y. H. & Lee, K. W.
1975
An aerosol generator of high stability. Am. Ind. Hyg. Assoc.
36, 861–865.

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.

Mariani, C., Vandenboomgaerde, M., Jourdan, G., Souffland, D. & Houas, L.
2008
Investigation of the Richtmyer–Meshkov instability with stereolithographed interfaces. Phys. Rev. Lett.
100, 254503.

Matsuoka, C., Nishihara, K. & Fukuda, Y.
2003
Nonlinear evolution of an interface in the Richtmyer–Meshkov instability. Phys. Rev. E
67, 036301.

McFarland, J. A., Greenough, J. A. & Ranjan, D.
2011
Computational parametric study of a Richtmyer–Meshkov instability for an inclined interface. Phys. Rev. E
84, 026303.

Meshkov, E. E.
1969
Instability of the interface of two gases accelerated by a shock wave. Izv. Akad. Nauk. SSSR Maekh. Zhidk. Gaza.
4, 151–157.

Meyer, K. A. & Blewett, P. J.
1972
Numerical investigation of the stability of a shock-accelerated interface between two fluids. Phys. Fluids
15, 753–759.

Mikaelian, K. O.
2003
Explicit expressions for the evolution of single-mode Rayleigh–Taylor and Richtmyer–Meshkov instabilities at arbitrary Atwood numbers. Phys. Rev. E
67, 026319.

Mirels, H.
1956
Attenuation in a shock-tube due to unsteady-boundary-layer action. NACA TN3278.

Mirels, H. & Braun, W. H.
1957
Nonuniformities in shock-tube flow due to unsteady-boundary-layer action. NACA TN4021.

Motl, B., Niederhaus, J., Ranjan, D., Oakley, J., Anderson, M. & Bonazza, R.
2007
Experimental studies for ICF related Richtmyer–Meshkov instabilities. Fus. Sci. Tech.
52, 1079–1083.

Nishihara, K., Wouchuk, J. G., Matsuoka, C., Ishizaki, R. & Zhakhovsky, V. V.
2010
Richtmyer–Meshkov instability: theory of linear and nonlinear evolution. Phil. Trans. R. Soc. A
368, 1769–1807.

Oron, D., Arazi, L., Kartoon, D., Rkanati, A., Alon, U. & Shvarts, D.
2001
Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling laws. Phys. Plasmas
8, 2108–2115.

Peng, G., Zabusky, N. J. & Zhang, S.
2003
Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface. Phys. Fluids
15, 3730–3744.

Prasad, J. K., Rasheed, A., Kumar, S. & Sturtevant, B.
2000
The late-time development of the Richtmyer–Meshkov instability. Phys. Fluids
12, 3730–3744.

Raffel, M., Kompenhans, J. & Willert, C. E.
1998
Particle Image Velocimetry: A Practical Guide. Springer.

Rayleigh, Lord
1900
Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density. Cambridge University Press.

Richtmyer, R. D.
1960
Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math.
23, 297–319.

Roshko, A.
1960
On flow duration in low-pressure shock tubes. Phys. Fluids
3, 835–842.

Sadot, O., Erez, L., Alon, U., Oron, D., Levin, L. A., Erez, G., Ben-Dor, B. & Shvarts, D.
1998
Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer–Meshkov instability. Phys. Rev. Lett.
80, 1654–1657.

Schlichting, H. & Gersten, K.
2000
Boundary-Layer Theory, 8th edn. Springer.

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

Sharp, R. W. Jr & Barton, R. T.
1981 Hemp advection model. UCID-17809 Rev.1, Lawrence Livermore Laboratory.

Sohn, S.-I.
2011
Inviscid and viscous vortex models for Richtmyer–Meshkov instability. Fluid Dyn. Res.
43, 065506.

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

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.

Tomkins, C., Kumar, S., Orlicz, G. & Prestridge, K.
2008
An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech.
611, 131–150.

von Kármán, T.
1921
Laminar and turbulent friction. Z. Angew. Math. Mech.
1, 233–252.

Vandenboomgaerde, M., Gauthier, S. & Mügler, C
2002
Nonlinear regime of a multimode Richtmyer–Meshkov instability: a simplified perturbation theory. Phys. Fluids
14, 1111–1122.

Vetter, M. & Sturtevant, B.
1995
Experiments on the Richtmyer–Meshkov instability of an air/
${\mathrm{SF} }_{6} $
interface. Shock Waves
4, 247–252.
Westerweel, J.
1993 Digital particle image velocimetry, theory and application. PhD thesis, Technische Universiteit Delft.

Wilkins, M. L.
1963 Calculation of elastic–plastic flow. UCRL-7322, Lawrence Radiation Laboratory.

Wouchuk, J. G. & Nishihara, K.
1997
Asymptotic growth in the linear Richtmyer–Meshkov instability. Phys. Plasmas
4, 1028–1038.

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

Zhang, Q. & Sohn, S.-I.
1997a
Nonlinear theory of unstable fluid mixing driven by shock wave. Phys. Fluids
9, 1106–1124.

Zhang, Q. & Sohn, S.-I.
1997b
Padé approximation to an interfacial fluid mixing problem. Appl. Math. Lett.
10, 121–127.