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Hydrodynamic instability driven by two co-propagating shock waves across varying Atwood numbers

Published online by Cambridge University Press:  24 November 2025

Yinuo Xing ,
Zhiming Dong ,
He Wang Open the ORCID record for He Wang [Opens in a new window] ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Yinuo Xing
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China , Hefei 230026, PR China
Zhiming Dong
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China , Hefei 230026, PR China
He Wang*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China , Hefei 230026, PR China
Zhigang Zhai
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China , Hefei 230026, PR China
Xisheng Luo
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China , Hefei 230026, PR China State Key Laboratory of High-Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
*
Corresponding author: He Wang, ustchewang@ustc.edu.cn
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Abstract

The evolution mechanisms and suppression strategy of the Richtmyer–Meshkov instability (RMI) at heavy–light interfaces with varying Atwood numbers accelerated by two co-propagating shock waves are investigated through theoretical analysis and experimental evaluation. Existing models describing the complete evolution of once-shocked interfaces and the linear growth of twice-shocked interfaces are examined across low, moderate and high Atwood number regimes, and further refined based on detailed analyses of their limitations. Furthermore, an analytical model for describing the complete evolution of a twice-shocked interface (DS model) is developed through a comprehensive consideration of the shock-compression, start-up, linear and weakly nonlinear evolution processes. The combination of the refined models and DS model enables, for the first time, an accurate prediction of the complete evolution of interfaces subjected to two co-propagating shock waves. Building upon this, the parameter conditions required to manipulate the RMI with varying Atwood numbers are identified. Verification experiments confirm that suppressing the RMI growth at interfaces with various Atwood numbers via a same-side reshock is feasible and predictable. The present study may shed some light on strategies to suppress hydrodynamic instabilities in inertial confinement fusion through integrated adjustment of material densities and shock timings.

JFM classification

Compressible Flows: Shock waves

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JFM Papers
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Journal of Fluid Mechanics , Volume 1023 , 25 November 2025 , A34
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© The Author(s), 2025. Published by Cambridge University Press

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References

Bell, G.I. 1951 Taylor instability on cylinders and spheres in the small amplitude approximation, Tech. Rep. LA-1321. LANL Los Alamos Scientific Laboratory of the University of California.Google Scholar
Betti, R. & Hurricane, O.A. 2016 Inertial-confinement fusion with lasers. Nat. Phys. 12, 435–448.10.1038/nphys3736CrossRefGoogle Scholar
Betti, R., Zhou, C.D., Anderson, K.S., Perkins, L.J., Theobald, W. & Solodov, A.A. 2007 Shock ignition of thermonuclear fuel with high areal density. Phys. Rev. Lett. 98, 155001.10.1103/PhysRevLett.98.155001CrossRefGoogle ScholarPubMed
Cao, Q., Chen, C., Wang, H., Zhai, Z. & Luo, X. 2024 Interface evolution induced by two successive shocks under diverse reshock conditions. J. Fluid Mech. 999, A31.10.1017/jfm.2024.957CrossRefGoogle Scholar
Charakhch’yan, A.A. 2000 Richtmyer–Meshkov instability of an interface between two media due to passage of two successive shocks. J. Appl. Mech. Tech. Phys. 41, 23–31.10.1007/BF02465232CrossRefGoogle Scholar
Charakhch’yan, A.A. 2001 Reshocking at the non-linear stage of Richtmyer–Meshkov instability. Plasma Phys. Control. Fusion 43, 1169–1179.10.1088/0741-3335/43/9/301CrossRefGoogle Scholar
Chen, C., Xing, Y., Wang, H., Zhai, Z. & Luo, X. 2023 Experimental study on Richtmyer–Meshkov instability at a light–heavy interface over a wide range of Atwood numbers. J. Fluid Mech. 975, A29.10.1017/jfm.2023.869CrossRefGoogle Scholar
Cherne, F.J., Hammerberg, J.E., Andrews, M.J., Karkhanis, V. & Ramaprabhu, P. 2015 On shock driven jetting of liquid from non-sinusoidal surfaces into a vacuum. J. Appl. Phys. 118, 185901.10.1063/1.4934645CrossRefGoogle Scholar
Dimonte, G. & Ramaprabhu, P. 2010 Simulations and model of the nonlinear Richtmyer–Meshkov instability. Phys. Fluids 22, 014104.10.1063/1.3276269CrossRefGoogle Scholar
Ding, J., Liang, Y., Chen, M., Zhai, Z., Si, T. & Luo, X. 2018 Interaction of planar shock wave with three-dimensional heavy cylindrical bubble. Phys. Fluids 30, 106109.10.1063/1.5050091CrossRefGoogle Scholar
Ding, J., Si, T., Chen, M., Zhai, Z., Lu, X. & Luo, X. 2017 a On the interaction of a planar shock with a three-dimensional light gas cylinder. J. Fluid Mech. 828, 289–317.10.1017/jfm.2017.528CrossRefGoogle Scholar
Ding, J., Si, T., Yang, J., Lu, X., Zhai, Z. & Luo, X. 2017 b Measurement of a Richtmyer–Meshkov instability at an air–SF $_{6}$ interface in a semiannular shock tube. Phys. Rev. Lett. 119, 014501.10.1103/PhysRevLett.119.014501CrossRefGoogle Scholar
Feng, L., Xu, J., Zhai, Z. & Luo, X. 2021 Evolution of shock-accelerated double-layer gas cylinder. Phys. Fluids 33, 086105.10.1063/5.0062459CrossRefGoogle Scholar
Goncharov, V.N., Knauer, J.P., McKenty, P.W., Radha, P.B., Sangster, T.C., Skupsky, S., Betti, R., McCrory, R.L. & Meyerhofer, D.D. 2003 Improved performance of direct-drive inertial confinement fusion target designs with adiabat shaping using an intensity picket. Phys. Plasmas 10, 1906–1918.10.1063/1.1562166CrossRefGoogle Scholar
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, 55–79.10.1017/S0022112099004838CrossRefGoogle Scholar
Karkhanis, V. & Ramaprabhu, P. 2019 Ejecta velocities in twice-shocked liquid metals under extreme conditions: A hydrodynamic approach. Matter Radiat. Extremes 4, 044402.10.1063/1.5088162CrossRefGoogle Scholar
Karkhanis, V., Ramaprabhu, P., Buttler, W.T., Hammerberg, J.E., Cherne, F.J. & Andrews, M.J. 2017 Ejecta production from second shock: numerical simulations and experiments. J. Dyn. Behav. Mater. 3, 265–279.10.1007/s40870-017-0091-9CrossRefGoogle Scholar
Kritcher, A.L. et al. 2022 Design of inertial fusion implosions reaching the burning plasma regime. Nat. Phys. 18, 251–258.10.1038/s41567-021-01485-9CrossRefGoogle Scholar
Li, J., Chen, C., Zhai, Z. & Luo, X. 2024 Effects of compressibility on Richtmyer–Meshkov instability of heavy/light interface. Phys. Fluids 36, 056104.10.1063/5.0207779CrossRefGoogle Scholar
Lindl, J., Landen, O., Edwards, J., Moses, E., et al. 2014 Review of the National Ignition Campaign 2009–2012. Phys. Plasmas 21, 020501.10.1063/1.4865400CrossRefGoogle Scholar
Lindl, J.D., Amendt, P., Berger, R.L., Glendinning, S.G., Glenzer, S.H., Haan, S.W., Kauffman, R.L., Landen, O.L. & Suter, L.J. 2004 The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. Plasmas 11, 339–491.10.1063/1.1578638CrossRefGoogle Scholar
Lindl, J.D., McCrory, R.L. & Campbell, E.M. 1992 Progress toward ignition and burn propagation in inertial confinement fusion. Phys. Today 45, 32–40.10.1063/1.881318CrossRefGoogle Scholar
Lombardini, M. & Pullin, D.I. 2009 Startup process in the Richtmyer–Meshkov instability. Phys. Fluids 21, 044104.10.1063/1.3091943CrossRefGoogle Scholar
Lombardini, M., Pullin, D.I. & Meiron, D.I. 2014 Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth. J. Fluid Mech. 748, 85–112.10.1017/jfm.2014.161CrossRefGoogle Scholar
Merritt, E.C. et al. 2023 Same-sided successive-shock HED instability experiments. Phys. Plasmas 30, 072108.10.1063/5.0148228CrossRefGoogle Scholar
Meshkov, E.E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.10.1007/BF01015969CrossRefGoogle Scholar
Mikaelian, K.O. 1985 Richtmyer–Meshkov instabilities in stratified fluids. Phys. Rev. A 31, 410–419.10.1103/PhysRevA.31.410CrossRefGoogle ScholarPubMed
Mikaelian, K.O. 1994 Freeze-out and the effect of compressibility in the Richtmyer–Meshkov instability. Phys. Fluids 6, 356–368.10.1063/1.868091CrossRefGoogle Scholar
Mirels, H. 1956 Boundary layer behind shock or thin expansion wave moving into stationary fluid. NACA Tech. Rep. (TN 3712 NACA).Google Scholar
Murakami, M., Nagatomo, H., Azechi, H., Ogando, F., Perlado, M. & Eliezer, S. 2006 Innovative ignition scheme for ICF-impact fast ignition. Nucl. Fusion 46, 99–103.10.1088/0029-5515/46/1/011CrossRefGoogle Scholar
Nuckolls, J., Wood, L., Thiessen, A. & Zimmerman, G. 1972 Laser compression of matter to super-high densities: thermonuclear (CTR) applications. Nature 239, 139–142.10.1038/239139a0CrossRefGoogle Scholar
Plesset, M.S. 1954 On the stability of fluid flows with spherical symmetry. J. Appl. Phys. 25, 96–98.10.1063/1.1721529CrossRefGoogle Scholar
Probyn, M.G., Williams, R.J.R., Thornber, B., Drikakis, D. & Youngs, D.L. 2021 2D single-mode Richtmyer–Meshkov instability. Physica D 418, 132827.10.1016/j.physd.2020.132827CrossRefGoogle Scholar
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.Google Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297–319.10.1002/cpa.3160130207CrossRefGoogle Scholar
Rikanati, A., Oron, D., Sadot, O. & Shvarts, D. 2003 High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer–Meshkov instability. Phys. Rev. E 67, 026307.10.1103/PhysRevE.67.026307CrossRefGoogle ScholarPubMed
Samulski, C., Srinivasan, B., Manuel, M.J.E., Masti, R.L., Sauppe, J.P. & Kline, J. 2022 Deceleration-stage Rayleigh–Taylor growth in a background magnetic field studied in cylindrical and Cartesian geometries. Matt. Radiat. Extrem. 7, 026902.10.1063/5.0062168CrossRefGoogle Scholar
Schill, W.J. et al. 2024 Suppression of Richtmyer–Meshkov instability via special pairs of shocks and phase transitions. Phys. Rev. Lett. 132, 024001.10.1103/PhysRevLett.132.024001CrossRefGoogle ScholarPubMed
Si, T., Jiang, S., Cai, W., Wang, H. & Luo, X. 2025 Shock-tube experiments on strong-shock-driven single-mode Richtmyer–Meshkov instability. J. Fluid Mech. 1006, R1.10.1017/jfm.2025.36CrossRefGoogle Scholar
Tabak, M., Hammer, J., Glinsky, M.E., Kruer, W.L., Wilks, S.C., Woodworth, J., Campbell, E.M., Perry, M.D. & Mason, R.J. 1994 Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 1, 1626–1634.10.1063/1.870664CrossRefGoogle Scholar
Taylor, G. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201, 192–196.Google Scholar
Wang, H., Cao, Q., Chen, C., Zhai, Z. & Luo, X. 2022 Experimental study on a light–heavy interface evolution induced by two successive shock waves. J. Fluid Mech. 953, A15.10.1017/jfm.2022.945CrossRefGoogle Scholar
Wang, H., Wang, H., Zhai, Z. & Luo, X. 2023 a High-amplitude effect on Richtmyer–Meshkov instability at a single-mode heavy–light interface. Phys. Fluids 35, 126107.10.1063/5.0180581CrossRefGoogle Scholar
Wang, H., Wang, H., Zhai, Z. & Luo, X. 2023 b High-amplitude effect on single-mode Richtmyer–Meshkov instability of a light–heavy interface. Phys. Fluids 35, 016106.10.1063/5.0132145CrossRefGoogle Scholar
Wouchuk, J.G. 2001 Growth rate of the Richtmyer–Meshkov instability when a rarefaction is reflected. Phys. Plasmas 8, 2890–2907.10.1063/1.1369119CrossRefGoogle Scholar
Wouchuk, J.G. & Nishihara, K. 1997 Asymptotic growth in the linear Richtmyer–Meshkov instability. Phys. Plasmas 4, 1028–1038.10.1063/1.872191CrossRefGoogle Scholar
Xing, Y., Chen, C., Li, J., Wang, H., Zhai, Z. & Luo, X. 2025 Atwood-number dependence of the Richtmyer–Meshkov instability at a heavy–light single-mode interface. J. Fluid Mech. 1007, A54.10.1017/jfm.2025.107CrossRefGoogle Scholar
Yang, Y., Zhang, Q. & Sharp, D.H. 1994 Small amplitude theory of Richtmyer–Meshkov instability. Phys. Fluids 6, 1856–1873.10.1063/1.868245CrossRefGoogle Scholar
Zhai, Z., Chen, C., Xing, Y., Li, J., Cao, Q., Wang, H. & Luo, X. 2025 Manipulation of Richtmyer–Meshkov instability on a heavy–light interface via successive shocks. J. Fluid Mech. 1003, A9.10.1017/jfm.2024.1211CrossRefGoogle Scholar
Zhang, J. et al. 2020 Double-cone ignition scheme for inertial confinement fusion. Phil. Trans. R. Soc. A 378, 20200015.10.1098/rsta.2020.0015CrossRefGoogle ScholarPubMed
Zhou, Y. 2017 a Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–722, 1–136.Google Scholar
Zhou, Y. 2017 b Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723–725, 1–160.Google Scholar
Zhou, Y. 2024 Hydrodynamic Instabilities and Turbulence: Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz Mixing. Cambridge University Press.10.1017/9781108779135CrossRefGoogle Scholar
Zhou, Y., Sadler, J.D. & Hurricane, O.A. 2025 Instabilities and mixing in inertial confinement fusion. Annu. Rev. Fluid Mech. 57, 197–225.10.1146/annurev-fluid-022824-110008CrossRefGoogle Scholar
Zhou, Y. et al. 2019 Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities. Phys. Plasmas 26, 080901.10.1063/1.5088745CrossRefGoogle Scholar
Zhou, Y. et al. 2021 Rayleigh–Taylor and Richtmyer–Meshkov instabilities: a journey through scales. Physica D 423, 132838.10.1016/j.physd.2020.132838CrossRefGoogle Scholar
Zylstra, A.B. et al. 2022 Burning plasma achieved in inertial fusion. Nature 601, 542–548.10.1038/s41586-021-04281-wCrossRefGoogle ScholarPubMed