Simulations and model of the nonlinear Richtmyer–Meshkov instability

Dimonte, Guy; Ramaprabhu, P.

doi:10.1063/1.3276269

Title: Simulations and model of the nonlinear Richtmyer–Meshkov instability

Journal Article · 20 January 2010 · Physics of Fluids

DOI: https://doi.org/10.1063/1.3276269 · OSTI ID:1076442

Dimonte, Guy ^[1]; Ramaprabhu, P. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of North Carolina, Charlotte, NC (United States)

The nonlinear evolution of the Richtmyer-Meshkov (RM) instability is investigated using numerical simulations with the FLASH code in two-dimensions (2D). The purpose of the simulations is to develop an empiricial nonlinear model of the RM instability that is applicable to inertial confinement fusion (ICF) and ejecta formation, namely, at large Atwood number A and scaled initial amplitude kh_o (k ≡ wavenumber) of the perturbation. The FLASH code is first validated with a variety of RM experiments that evolve well into the nonlinear regime. They reveal that bubbles stagnate when they grow by an increment of 2/k and that spikes accelerate for A > 0.5 due to higher harmonics that focus them. These results are then compared with a variety of nonlinear models that are based on potential flow. We find that the models agree with simulations for moderate values of A < 0.9 and kh_o< 1, but not for the larger values that characterize ICF and ejecta formation. We thus develop a new nonlinear empirical model that captures the simulation results consistent with potential flow for a broader range of A and kh_o. Our hope is that such empirical models concisely capture the RM simulations and inspire more rigorous solutions.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1076442

Journal Information:: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 1 Vol. 22; ISSN 1070-6631; ISSN PHFLE6

Publisher:: American Institute of PhysicsCopyright Statement

Country of Publication:: United States

Language:: English

References (112)

Taylor instability in shock acceleration of compressible fluids Richtmyer, Robert D. Communications on Pure and Applied Mathematics, Vol. 13, Issue 2 https://doi.org/10.1002/cpa.3160130207	journal	May 1960
Instability of the interface of two gases accelerated by a shock wave Meshkov, E. E. Fluid Dynamics, Vol. 4, Issue 5 https://doi.org/10.1007/bf01015969	journal	January 1972
An analytical nonlinear theory of Richtmyer-Meshkov instability Zhang, Qiang; Sohn, Sung-Ik Physics Letters A, Vol. 212, Issue 3 https://doi.org/10.1016/0375-9601(96)00021-7	journal	March 1996
Experimental study of the Richtmyer–Meshkov instability of incompressible fluids Niederhaus, C. E.; Jacobs, J. W. Journal of Fluid Mechanics, Vol. 485 https://doi.org/10.1017/s002211200300452x	journal	May 2003
Richtmyer–Meshkov instability growth: experiment, simulation and theory Holmes, Richard L.; Dimonte, Guy; Fryxell, Bruce Journal of Fluid Mechanics, Vol. 389 https://doi.org/10.1017/s0022112099004838	journal	June 1999
Feedout and Richtmyer–Meshkov instability at large density difference Velikovich, Alexander L.; Schmitt, Andrew J.; Gardner, John H. Physics of Plasmas, Vol. 8, Issue 2 https://doi.org/10.1063/1.1335829	journal	February 2001
Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling laws Oron, D.; Arazi, L.; Kartoon, D. Physics of Plasmas, Vol. 8, Issue 6 https://doi.org/10.1063/1.1362529	journal	June 2001
Growth rate of the Richtmyer–Meshkov instability when a rarefaction is reflected Wouchuk, J. G. Physics of Plasmas, Vol. 8, Issue 6 https://doi.org/10.1063/1.1369119	journal	June 2001
Nonlinear regime of a multimode Richtmyer–Meshkov instability: A simplified perturbation theory Vandenboomgaerde, Marc; Gauthier, Serge; Mügler, Claude Physics of Fluids, Vol. 14, Issue 3 https://doi.org/10.1063/1.1447914	journal	March 2002
Effect of shock proximity on Richtmyer–Meshkov growth Glendinning, S. G.; Bolstad, J.; Braun, D. G. Physics of Plasmas, Vol. 10, Issue 5 https://doi.org/10.1063/1.1562165	journal	May 2003
Numerical Investigation of the Stability of a Shock-Accelerated Interface between Two Fluids Meyer, K. A. Physics of Fluids, Vol. 15, Issue 5 https://doi.org/10.1063/1.1693980	journal	January 1972
Experiments on the late-time development of single-mode Richtmyer–Meshkov instability Jacobs, J. W.; Krivets, V. V. Physics of Fluids, Vol. 17, Issue 3 https://doi.org/10.1063/1.1852574	journal	March 2005
A vortex model for Richtmyer–Meshkov instability accounting for finite Atwood number Likhachev, Oleg A.; Jacobs, Jeffrey W. Physics of Fluids, Vol. 17, Issue 3 https://doi.org/10.1063/1.1863276	journal	March 2005
Piezoelectric characterization of ejecta from shocked tin surfaces Vogan, W. S.; Anderson, W. W.; Grover, M. Journal of Applied Physics, Vol. 98, Issue 11 https://doi.org/10.1063/1.2132521	journal	December 2005
K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities Dimonte, Guy; Tipton, Robert Physics of Fluids, Vol. 18, Issue 8 https://doi.org/10.1063/1.2219768	journal	August 2006
High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions Latini, Marco; Schilling, Oleg; Don, Wai Sun Physics of Fluids, Vol. 19, Issue 2 https://doi.org/10.1063/1.2472508	journal	February 2007
Probing the underlying physics of ejecta production from shocked Sn samples Zellner, M. B.; McNeil, W. Vogan; Hammerberg, J. E. Journal of Applied Physics, Vol. 103, Issue 12 https://doi.org/10.1063/1.2939253	journal	June 2008
Rayleigh–Taylor stability for a normal shock wave–density discontinuity interaction Fraley, Gary Physics of Fluids, Vol. 29, Issue 2 https://doi.org/10.1063/1.865722	journal	January 1986
Freeze‐out and the effect of compressibility in the Richtmyer–Meshkov instability Mikaelian, Karnig O. Physics of Fluids, Vol. 6, Issue 1 https://doi.org/10.1063/1.868091	journal	January 1994
Small amplitude theory of Richtmyer–Meshkov instability Yang, Yumin; Zhang, Qiang; Sharp, David H. Physics of Fluids, Vol. 6, Issue 5 https://doi.org/10.1063/1.868245	journal	May 1994
Nonlinear theory of unstable fluid mixing driven by shock wave Zhang, Qiang; Sohn, Sung-Ik Physics of Fluids, Vol. 9, Issue 4 https://doi.org/10.1063/1.869202	journal	April 1997
Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories Dimonte, Guy; Schneider, Marilyn Physics of Fluids, Vol. 12, Issue 2 https://doi.org/10.1063/1.870309	journal	February 2000
Richtmyer–Meshkov instability with strong radiatively driven shocks Dimonte, Guy; Frerking, C. Eric; Schneider, Marilyn Physics of Plasmas, Vol. 3, Issue 2 https://doi.org/10.1063/1.871889	journal	February 1996
Asymptotic growth in the linear Richtmyer–Meshkov instability Wouchuk, Juan Gustavo; Nishihara, Katsunobu Physics of Plasmas, Vol. 4, Issue 4 https://doi.org/10.1063/1.872191	journal	April 1997
On the Instability of Superposed Fluids in a Gravitational Field. Layzer, David The Astrophysical Journal, Vol. 122 https://doi.org/10.1086/146048	journal	July 1955
The Physics of Inertial Fusion Atzeni, Stefano; Meyer-ter-Vehn, Jürgen https://doi.org/10.1093/acprof:oso/9780198562641.001.0001	book	January 2004
Impulsive model for the Richtmyer-Meshkov instability Vandenboomgaerde, Marc; Mügler, Claude; Gauthier, Serge Physical Review E, Vol. 58, Issue 2 https://doi.org/10.1103/physreve.58.1874	journal	August 1998
Growth rate of the linear Richtmyer-Meshkov instability when a shock is reflected Wouchuk, J. G. Physical Review E, Vol. 63, Issue 5 https://doi.org/10.1103/physreve.63.056303	journal	April 2001
Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios Sohn, Sung-Ik Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/physreve.67.026301	journal	February 2003
High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer-Meshkov instability Rikanati, A.; Oron, D.; Sadot, O. Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/physreve.67.026307	journal	February 2003
Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers Mikaelian, Karnig O. Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/physreve.67.026319	journal	February 2003
Nonlinear evolution of an interface in the Richtmyer-Meshkov instability Matsuoka, Chihiro; Nishihara, Katsunobu; Fukuda, Yuko Physical Review E, Vol. 67, Issue 3 https://doi.org/10.1103/physreve.67.036301	journal	March 2003
Erratum: Nonlinear evolution of an interface in the Richtmyer-Meshkov instability [Phys. Rev. E 67 , 036301 (2003)] Matsuoka, Chihiro; Nishihara, Katsunobu; Fukuda, Yuko Physical Review E, Vol. 68, Issue 2 https://doi.org/10.1103/physreve.68.029902	journal	August 2003
Density dependence of a Zufiria-type model for Rayleigh–Taylor bubble fronts Sohn, Sung-Ik Physical Review E, Vol. 70, Issue 4 https://doi.org/10.1103/physreve.70.045301	journal	October 2004
Limitations and failures of the Layzer model for hydrodynamic instabilities Mikaelian, Karnig O. Physical Review E, Vol. 78, Issue 1 https://doi.org/10.1103/physreve.78.015303	journal	July 2008
Investigation of the Richtmyer-Meshkov Instability with Stereolithographed Interfaces Mariani, Christian; Vandenboomgaerde, Marc; Jourdan, Georges Physical Review Letters, Vol. 100, Issue 25 https://doi.org/10.1103/physrevlett.100.254503	journal	June 2008
Richtmyer-Meshkov experiments on the Nova laser at high compression Dimonte, Guy; Remington, Bruce Physical Review Letters, Vol. 70, Issue 12 https://doi.org/10.1103/physrevlett.70.1806	journal	March 1993
Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios Alon, U.; Hecht, J.; Ofer, D. Physical Review Letters, Vol. 74, Issue 4 https://doi.org/10.1103/physrevlett.74.534	journal	January 1995
Nonlinear Perturbation Theory of the Incompressible Richtmyer-Meshkov Instability Velikovich, Alexander L.; Dimonte, Guy Physical Review Letters, Vol. 76, Issue 17 https://doi.org/10.1103/physrevlett.76.3112	journal	April 1996
Study of Nonlinear Evolution of Single-Mode and Two-Bubble Interaction under Richtmyer-Meshkov Instability Sadot, O.; Erez, L.; Alon, U. Physical Review Letters, Vol. 80, Issue 8 https://doi.org/10.1103/physrevlett.80.1654	journal	February 1998
Analytic Approach to Nonlinear Rayleigh-Taylor and Richtmyer-Meshkov Instabilities Mikaelian, Karnig O. Physical Review Letters, Vol. 80, Issue 3 https://doi.org/10.1103/physrevlett.80.508	journal	January 1998
Analytical Solutions of Layzer-Type Approach to Unstable Interfacial Fluid Mixing Zhang, Qiang Physical Review Letters, Vol. 81, Issue 16 https://doi.org/10.1103/physrevlett.81.3391	journal	October 1998
Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers Goncharov, V. N. Physical Review Letters, Vol. 88, Issue 13 https://doi.org/10.1103/physrevlett.88.134502	journal	March 2002
Shock Ignition of Thermonuclear Fuel with High Areal Density Betti, R.; Zhou, C. D.; Anderson, K. S. Physical Review Letters, Vol. 98, Issue 15 https://doi.org/10.1103/physrevlett.98.155001	journal	April 2007
Validating astrophysical simulation codes Calder, A.; Dursi, J.; Fryxell, B. Computing in Science and Engineering, Vol. 6, Issue 5 https://doi.org/10.1109/mcse.2004.44	journal	September 2004
Taylor instability in shock acceleration of compressible fluids Richtmyer, Robert D. Communications on Pure and Applied Mathematics, Vol. 13, Issue 2 https://doi.org/10.1002/cpa.3160130207	journal	May 1960
Instability of the interface of two gases accelerated by a shock wave Meshkov, E. E. Fluid Dynamics, Vol. 4, Issue 5 https://doi.org/10.1007/BF01015969	journal	January 1972
Instability of the interface of two gases accelerated by a shock wave Meshkov, E. E. Fluid Dynamics, Vol. 4, Issue 5 https://doi.org/10.1007/bf01015969	journal	January 1972
An analytical nonlinear theory of Richtmyer-Meshkov instability Zhang, Qiang; Sohn, Sung-Ik Physics Letters A, Vol. 212, Issue 3 https://doi.org/10.1016/0375-9601(96)00021-7	journal	March 1996
Experimental study of the Richtmyer–Meshkov instability of incompressible fluids Niederhaus, C. E.; Jacobs, J. W. Journal of Fluid Mechanics, Vol. 485 https://doi.org/10.1017/S002211200300452X	journal	May 2003
Richtmyer–Meshkov instability growth: experiment, simulation and theory Holmes, Richard L.; Dimonte, Guy; Fryxell, Bruce Journal of Fluid Mechanics, Vol. 389 https://doi.org/10.1017/S0022112099004838	journal	June 1999
Experimental study of the Richtmyer–Meshkov instability of incompressible fluids Niederhaus, C. E.; Jacobs, J. W. Journal of Fluid Mechanics, Vol. 485 https://doi.org/10.1017/s002211200300452x	journal	May 2003
Richtmyer–Meshkov instability growth: experiment, simulation and theory Holmes, Richard L.; Dimonte, Guy; Fryxell, Bruce Journal of Fluid Mechanics, Vol. 389 https://doi.org/10.1017/s0022112099004838	journal	June 1999
Feedout and Richtmyer–Meshkov instability at large density difference Velikovich, Alexander L.; Schmitt, Andrew J.; Gardner, John H. Physics of Plasmas, Vol. 8, Issue 2 https://doi.org/10.1063/1.1335829	journal	February 2001
Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling laws Oron, D.; Arazi, L.; Kartoon, D. Physics of Plasmas, Vol. 8, Issue 6 https://doi.org/10.1063/1.1362529	journal	June 2001
Growth rate of the Richtmyer–Meshkov instability when a rarefaction is reflected Wouchuk, J. G. Physics of Plasmas, Vol. 8, Issue 6 https://doi.org/10.1063/1.1369119	journal	June 2001
Nonlinear regime of a multimode Richtmyer–Meshkov instability: A simplified perturbation theory Vandenboomgaerde, Marc; Gauthier, Serge; Mügler, Claude Physics of Fluids, Vol. 14, Issue 3 https://doi.org/10.1063/1.1447914	journal	March 2002
Effect of shock proximity on Richtmyer–Meshkov growth Glendinning, S. G.; Bolstad, J.; Braun, D. G. Physics of Plasmas, Vol. 10, Issue 5 https://doi.org/10.1063/1.1562165	journal	May 2003
Numerical Investigation of the Stability of a Shock-Accelerated Interface between Two Fluids Meyer, K. A. Physics of Fluids, Vol. 15, Issue 5 https://doi.org/10.1063/1.1693980	journal	January 1972
Experiments on the late-time development of single-mode Richtmyer–Meshkov instability Jacobs, J. W.; Krivets, V. V. Physics of Fluids, Vol. 17, Issue 3 https://doi.org/10.1063/1.1852574	journal	March 2005
A vortex model for Richtmyer–Meshkov instability accounting for finite Atwood number Likhachev, Oleg A.; Jacobs, Jeffrey W. Physics of Fluids, Vol. 17, Issue 3 https://doi.org/10.1063/1.1863276	journal	March 2005
Piezoelectric characterization of ejecta from shocked tin surfaces Vogan, W. S.; Anderson, W. W.; Grover, M. Journal of Applied Physics, Vol. 98, Issue 11 https://doi.org/10.1063/1.2132521	journal	December 2005
K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities Dimonte, Guy; Tipton, Robert Physics of Fluids, Vol. 18, Issue 8 https://doi.org/10.1063/1.2219768	journal	August 2006
High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions Latini, Marco; Schilling, Oleg; Don, Wai Sun Physics of Fluids, Vol. 19, Issue 2 https://doi.org/10.1063/1.2472508	journal	February 2007
Probing the underlying physics of ejecta production from shocked Sn samples Zellner, M. B.; McNeil, W. Vogan; Hammerberg, J. E. Journal of Applied Physics, Vol. 103, Issue 12 https://doi.org/10.1063/1.2939253	journal	June 2008
Rayleigh–Taylor stability for a normal shock wave–density discontinuity interaction Fraley, Gary Physics of Fluids, Vol. 29, Issue 2 https://doi.org/10.1063/1.865722	journal	January 1986
Freeze‐out and the effect of compressibility in the Richtmyer–Meshkov instability Mikaelian, Karnig O. Physics of Fluids, Vol. 6, Issue 1 https://doi.org/10.1063/1.868091	journal	January 1994
Small amplitude theory of Richtmyer–Meshkov instability Yang, Yumin; Zhang, Qiang; Sharp, David H. Physics of Fluids, Vol. 6, Issue 5 https://doi.org/10.1063/1.868245	journal	May 1994
Nonlinear theory of unstable fluid mixing driven by shock wave Zhang, Qiang; Sohn, Sung-Ik Physics of Fluids, Vol. 9, Issue 4 https://doi.org/10.1063/1.869202	journal	April 1997
Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories Dimonte, Guy; Schneider, Marilyn Physics of Fluids, Vol. 12, Issue 2 https://doi.org/10.1063/1.870309	journal	February 2000
Richtmyer–Meshkov instability with strong radiatively driven shocks Dimonte, Guy; Frerking, C. Eric; Schneider, Marilyn Physics of Plasmas, Vol. 3, Issue 2 https://doi.org/10.1063/1.871889	journal	February 1996
Asymptotic growth in the linear Richtmyer–Meshkov instability Wouchuk, Juan Gustavo; Nishihara, Katsunobu Physics of Plasmas, Vol. 4, Issue 4 https://doi.org/10.1063/1.872191	journal	April 1997
On the Instability of Superposed Fluids in a Gravitational Field. Layzer, David The Astrophysical Journal, Vol. 122 https://doi.org/10.1086/146048	journal	July 1955
The Physics of Inertial Fusion Atzeni, Stefano; Meyer-ter-Vehn, Jürgen https://doi.org/10.1093/acprof:oso/9780198562641.001.0001	book	January 2004
Impulsive model for the Richtmyer-Meshkov instability Vandenboomgaerde, Marc; Mügler, Claude; Gauthier, Serge Physical Review E, Vol. 58, Issue 2 https://doi.org/10.1103/PhysRevE.58.1874	journal	August 1998
Growth rate of the linear Richtmyer-Meshkov instability when a shock is reflected Wouchuk, J. G. Physical Review E, Vol. 63, Issue 5 https://doi.org/10.1103/PhysRevE.63.056303	journal	April 2001
Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios Sohn, Sung-Ik Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/PhysRevE.67.026301	journal	February 2003
High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer-Meshkov instability Rikanati, A.; Oron, D.; Sadot, O. Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/PhysRevE.67.026307	journal	February 2003
Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers Mikaelian, Karnig O. Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/PhysRevE.67.026319	journal	February 2003
Nonlinear evolution of an interface in the Richtmyer-Meshkov instability Matsuoka, Chihiro; Nishihara, Katsunobu; Fukuda, Yuko Physical Review E, Vol. 67, Issue 3 https://doi.org/10.1103/PhysRevE.67.036301	journal	March 2003
Erratum: Nonlinear evolution of an interface in the Richtmyer-Meshkov instability [Phys. Rev. E 67 , 036301 (2003)] Matsuoka, Chihiro; Nishihara, Katsunobu; Fukuda, Yuko Physical Review E, Vol. 68, Issue 2 https://doi.org/10.1103/PhysRevE.68.029902	journal	August 2003
Density dependence of a Zufiria-type model for Rayleigh–Taylor bubble fronts Sohn, Sung-Ik Physical Review E, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevE.70.045301	journal	October 2004
Limitations and failures of the Layzer model for hydrodynamic instabilities Mikaelian, Karnig O. Physical Review E, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevE.78.015303	journal	July 2008
Investigation of the Richtmyer-Meshkov Instability with Stereolithographed Interfaces Mariani, Christian; Vandenboomgaerde, Marc; Jourdan, Georges Physical Review Letters, Vol. 100, Issue 25 https://doi.org/10.1103/PhysRevLett.100.254503	journal	June 2008
Richtmyer-Meshkov experiments on the Nova laser at high compression Dimonte, Guy; Remington, Bruce Physical Review Letters, Vol. 70, Issue 12 https://doi.org/10.1103/PhysRevLett.70.1806	journal	March 1993
Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios Alon, U.; Hecht, J.; Ofer, D. Physical Review Letters, Vol. 74, Issue 4 https://doi.org/10.1103/PhysRevLett.74.534	journal	January 1995
Nonlinear Perturbation Theory of the Incompressible Richtmyer-Meshkov Instability Velikovich, Alexander L.; Dimonte, Guy Physical Review Letters, Vol. 76, Issue 17 https://doi.org/10.1103/PhysRevLett.76.3112	journal	April 1996
Study of Nonlinear Evolution of Single-Mode and Two-Bubble Interaction under Richtmyer-Meshkov Instability Sadot, O.; Erez, L.; Alon, U. Physical Review Letters, Vol. 80, Issue 8 https://doi.org/10.1103/PhysRevLett.80.1654	journal	February 1998
Analytic Approach to Nonlinear Rayleigh-Taylor and Richtmyer-Meshkov Instabilities Mikaelian, Karnig O. Physical Review Letters, Vol. 80, Issue 3 https://doi.org/10.1103/PhysRevLett.80.508	journal	January 1998
Analytical Solutions of Layzer-Type Approach to Unstable Interfacial Fluid Mixing Zhang, Qiang Physical Review Letters, Vol. 81, Issue 16 https://doi.org/10.1103/PhysRevLett.81.3391	journal	October 1998
Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers Goncharov, V. N. Physical Review Letters, Vol. 88, Issue 13 https://doi.org/10.1103/PhysRevLett.88.134502	journal	March 2002
Shock Ignition of Thermonuclear Fuel with High Areal Density Betti, R.; Zhou, C. D.; Anderson, K. S. Physical Review Letters, Vol. 98, Issue 15 https://doi.org/10.1103/PhysRevLett.98.155001	journal	April 2007
Impulsive model for the Richtmyer-Meshkov instability Vandenboomgaerde, Marc; Mügler, Claude; Gauthier, Serge Physical Review E, Vol. 58, Issue 2 https://doi.org/10.1103/physreve.58.1874	journal	August 1998
Growth rate of the linear Richtmyer-Meshkov instability when a shock is reflected Wouchuk, J. G. Physical Review E, Vol. 63, Issue 5 https://doi.org/10.1103/physreve.63.056303	journal	April 2001
Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios Sohn, Sung-Ik Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/physreve.67.026301	journal	February 2003
High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer-Meshkov instability Rikanati, A.; Oron, D.; Sadot, O. Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/physreve.67.026307	journal	February 2003
Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers Mikaelian, Karnig O. Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/physreve.67.026319	journal	February 2003
Nonlinear evolution of an interface in the Richtmyer-Meshkov instability Matsuoka, Chihiro; Nishihara, Katsunobu; Fukuda, Yuko Physical Review E, Vol. 67, Issue 3 https://doi.org/10.1103/physreve.67.036301	journal	March 2003
Erratum: Nonlinear evolution of an interface in the Richtmyer-Meshkov instability [Phys. Rev. E 67 , 036301 (2003)] Matsuoka, Chihiro; Nishihara, Katsunobu; Fukuda, Yuko Physical Review E, Vol. 68, Issue 2 https://doi.org/10.1103/physreve.68.029902	journal	August 2003
Density dependence of a Zufiria-type model for Rayleigh–Taylor bubble fronts Sohn, Sung-Ik Physical Review E, Vol. 70, Issue 4 https://doi.org/10.1103/physreve.70.045301	journal	October 2004
Limitations and failures of the Layzer model for hydrodynamic instabilities Mikaelian, Karnig O. Physical Review E, Vol. 78, Issue 1 https://doi.org/10.1103/physreve.78.015303	journal	July 2008
Investigation of the Richtmyer-Meshkov Instability with Stereolithographed Interfaces Mariani, Christian; Vandenboomgaerde, Marc; Jourdan, Georges Physical Review Letters, Vol. 100, Issue 25 https://doi.org/10.1103/physrevlett.100.254503	journal	June 2008
Richtmyer-Meshkov experiments on the Nova laser at high compression Dimonte, Guy; Remington, Bruce Physical Review Letters, Vol. 70, Issue 12 https://doi.org/10.1103/physrevlett.70.1806	journal	March 1993
Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios Alon, U.; Hecht, J.; Ofer, D. Physical Review Letters, Vol. 74, Issue 4 https://doi.org/10.1103/physrevlett.74.534	journal	January 1995
Nonlinear Perturbation Theory of the Incompressible Richtmyer-Meshkov Instability Velikovich, Alexander L.; Dimonte, Guy Physical Review Letters, Vol. 76, Issue 17 https://doi.org/10.1103/physrevlett.76.3112	journal	April 1996
Study of Nonlinear Evolution of Single-Mode and Two-Bubble Interaction under Richtmyer-Meshkov Instability Sadot, O.; Erez, L.; Alon, U. Physical Review Letters, Vol. 80, Issue 8 https://doi.org/10.1103/physrevlett.80.1654	journal	February 1998
Analytic Approach to Nonlinear Rayleigh-Taylor and Richtmyer-Meshkov Instabilities Mikaelian, Karnig O. Physical Review Letters, Vol. 80, Issue 3 https://doi.org/10.1103/physrevlett.80.508	journal	January 1998
Analytical Solutions of Layzer-Type Approach to Unstable Interfacial Fluid Mixing Zhang, Qiang Physical Review Letters, Vol. 81, Issue 16 https://doi.org/10.1103/physrevlett.81.3391	journal	October 1998
Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers Goncharov, V. N. Physical Review Letters, Vol. 88, Issue 13 https://doi.org/10.1103/physrevlett.88.134502	journal	March 2002
Shock Ignition of Thermonuclear Fuel with High Areal Density Betti, R.; Zhou, C. D.; Anderson, K. S. Physical Review Letters, Vol. 98, Issue 15 https://doi.org/10.1103/physrevlett.98.155001	journal	April 2007
Validating astrophysical simulation codes Calder, A.; Dursi, J.; Fryxell, B. Computing in Science and Engineering, Vol. 6, Issue 5 https://doi.org/10.1109/MCSE.2004.44	journal	September 2004
Validating astrophysical simulation codes Calder, A.; Dursi, J.; Fryxell, B. Computing in Science and Engineering, Vol. 6, Issue 5 https://doi.org/10.1109/mcse.2004.44	journal	September 2004

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Unstable Richtmyer–Meshkov growth of solid and liquid metals in vacuum Buttler, W. T.; Oró, D. M.; Preston, D. L. Journal of Fluid Mechanics, Vol. 703 https://doi.org/10.1017/jfm.2012.190	journal	June 2012
On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments Morgan, Robert V.; Aure, R.; Stockero, J. D. Journal of Fluid Mechanics, Vol. 712 https://doi.org/10.1017/jfm.2012.426	journal	October 2012
Perturbation theory and numerical modelling of weakly and moderately nonlinear dynamics of the incompressible Richtmyer–Meshkov instability Velikovich, A. L.; Herrmann, M.; Abarzhi, S. I. Journal of Fluid Mechanics, Vol. 751 https://doi.org/10.1017/jfm.2014.312	journal	June 2014
The Richtmyer–Meshkov instability of a ‘V’ shaped air/ interface Luo, Xisheng; Dong, Ping; Si, Ting Journal of Fluid Mechanics, Vol. 802 https://doi.org/10.1017/jfm.2016.476	journal	August 2016
An elaborate experiment on the single-mode Richtmyer–Meshkov instability Liu, Lili; Liang, Yu; Ding, Juchun Journal of Fluid Mechanics, Vol. 853 https://doi.org/10.1017/jfm.2018.628	journal	August 2018
Effects of non-periodic portions of interface on Richtmyer–Meshkov instability Luo, Xisheng; Liang, Yu; Si, Ting Journal of Fluid Mechanics, Vol. 861 https://doi.org/10.1017/jfm.2018.923	journal	December 2018
Ejecta source model based on the nonlinear Richtmyer-Meshkov instability Dimonte, Guy; Terrones, Guillermo; Cherne, F. J. Journal of Applied Physics, Vol. 113, Issue 2 https://doi.org/10.1063/1.4773575	journal	January 2013
Power law and exponential ejecta size distributions from the dynamic fragmentation of shock-loaded Cu and Sn metals under melt conditions Durand, O.; Soulard, L. Journal of Applied Physics, Vol. 114, Issue 19 https://doi.org/10.1063/1.4832758	journal	November 2013
An experimental and numerical investigation of the dependency on the initial conditions of the Richtmyer-Meshkov instability Vandenboomgaerde, Marc; Souffland, Denis; Mariani, Christian Physics of Fluids, Vol. 26, Issue 2 https://doi.org/10.1063/1.4865836	journal	February 2014
Numerical simulations of the two-dimensional multimode Richtmyer-Meshkov instability Thornber, B.; Zhou, Y. Physics of Plasmas, Vol. 22, Issue 3 https://doi.org/10.1063/1.4915517	journal	March 2015
The Richtmyer-Meshkov instability of a “V” shaped air/helium interface subjected to a weak shock Zhai, Zhigang; Dong, Ping; Si, Ting Physics of Fluids, Vol. 28, Issue 8 https://doi.org/10.1063/1.4961038	journal	August 2016
PDV-based estimation of ejecta particles’ mass-velocity function from shock-loaded tin experiment Franzkowiak, J. -E.; Prudhomme, G.; Mercier, P. Review of Scientific Instruments, Vol. 89, Issue 3 https://doi.org/10.1063/1.4997365	journal	March 2018
A numerical study of bubble and spike velocities in shock-driven liquid metals Karkhanis, V.; Ramaprabhu, P.; Cherne, F. J. Journal of Applied Physics, Vol. 123, Issue 2 https://doi.org/10.1063/1.5008495	journal	January 2018
Molecular-dynamics simulation of Richtmyer-Meshkov instability on a Li-H ₂ interface at extreme compressing conditions Huang, Shenghong; Wang, Weirong; Luo, Xisheng Physics of Plasmas, Vol. 25, Issue 6 https://doi.org/10.1063/1.5018845	journal	June 2018
Ejecta velocities in twice-shocked liquid metals under extreme conditions: A hydrodynamic approach Karkhanis, V.; Ramaprabhu, P. Matter and Radiation at Extremes, Vol. 4, Issue 4 https://doi.org/10.1063/1.5088162	journal	July 2019
Spike Penetration in Blast-Wave-Driven Instabilities Drake, R. P. The Astrophysical Journal, Vol. 744, Issue 2 https://doi.org/10.1088/0004-637x/744/2/184	journal	December 2011
Statistically heterogeneous size distribution of ejecta from shock-loaded Cu with a wedged surface groove He, An-Min; Wang, Pei; Shao, Jian-Li Modelling and Simulation in Materials Science and Engineering, Vol. 24, Issue 2 https://doi.org/10.1088/0965-0393/24/2/025002	journal	January 2016
Heterogeneous fragmentation of metallic liquid microsheet with high velocity gradient He, An-Min; Wang, Pei; Shao, Jian-Li Chinese Physics B, Vol. 25, Issue 1 https://doi.org/10.1088/1674-1056/25/1/017102	journal	January 2016
Scale-to-scale energy transfer in mixing flow induced by the Richtmyer-Meshkov instability Liu, Han; Xiao, Zuoli Physical Review E, Vol. 93, Issue 5 https://doi.org/10.1103/physreve.93.053112	journal	May 2016
Bubble merger in initial Richtmyer-Meshkov instability on inverse-chevron interface Guo, Xu; Zhai, Zhigang; Si, Ting Physical Review Fluids, Vol. 4, Issue 9 https://doi.org/10.1103/physrevfluids.4.092001	journal	September 2019

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Title: Simulations and model of the nonlinear Richtmyer–Meshkov instability

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