Hostname: page-component-7857688df4-mqpdw Total loading time: 0 Render date: 2025-11-17T13:48:03.598Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling and mechanism of non-standard Richtmyer–Meshkov instability at heavy–light interfaces under moderate Mach numbers

Published online by Cambridge University Press:  12 November 2025

Jiaxuan Li Open the ORCID record for Jiaxuan Li [Opens in a new window]  and
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window]
Jiaxuan Li
Affiliation:
State Key Laboratory of High-Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
Zhigang Zhai*
Affiliation:
State Key Laboratory of High-Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
*
Corresponding author: Zhigang Zhai, sanjing@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

This study presents an analytical advancement in predicting the growth rate of perturbation amplitude in two-dimensional non-standard Richtmyer–Meshkov instability (RMI), driven by the interaction of a first-phase rippled shock wave at moderate Mach number with a heavy–light interface. We extend the irrotational model to encompass non-standard RMI scenarios, establishing a generalised framework validated through numerical simulations. Distinct from previous models, our model is free of empirical coefficients, and demonstrates superior accuracy across diverse perturbation configurations and Mach numbers. The analyses reveal the fundamental disparity of non-standard RMI from classical RMI: the vorticity deposition mechanism in non-standard RMI arises not only from normal pressure gradients at the shock front but crucially from tangential pressure gradients behind the shock wave. The asymptotic circulations are also well predicted by our model. Moreover, the relationship of the amplitudes between sinusoidal shock and perturbed interface is derived based on the model to realise the freeze-out of interface amplitude. The initial fundamental mode’s amplitude growth is frozen well, and the mixing width is greatly suppressed.

JFM classification

Compressible Flows: Shock waves

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1023 , 25 November 2025 , A6
Check for updates
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abarzhi, S.I., Bhowmick, A.K., Naveh, A., Pandian, A., Swisher, N.C., Stellingwerf, R.F. & Arnett, W.D. 2019 Supernova, nuclear synthesis, fluid instabilities, and interfacial mixing. Proc. Natl Acad. Sci. 116, 18184–18192.10.1073/pnas.1714502115CrossRefGoogle ScholarPubMed
Andrés, C.-R., Alexander, L.V. & César, H. 2023 On the stability of piston-driven planar shocks. J. Fluid Mech. 964, A33.Google Scholar
Bates, J.W. 2004 Initial value problem solution for isolated rippled shock fronts in arbitrary fluid media. Phys. Rev. E 69, 056313.10.1103/PhysRevE.69.056313CrossRefGoogle ScholarPubMed
Briscoe, M.G. & Kovitz, A.A. 1968 Experimental and theoretical study of the stability of plane shock waves reflected normally from perturbed flat walls. J. Fluid Mech. 31, 529–546.10.1017/S0022112068000315CrossRefGoogle Scholar
Campbell, E.M., et al. 2021 Direct-drive laser fusion: status, plans and future. Phil. Trans. R. Soc. A 379, 20200011.10.1098/rsta.2020.0011CrossRefGoogle ScholarPubMed
Chen, C., Wang, H., Zhai, Z. & Luo, X. 2024 Mode coupling between two different interfaces of a gas layer subject to a shock. J. Fluid Mech. 984, A38.10.1017/jfm.2024.232CrossRefGoogle Scholar
Ding, J., Si, T., Chen, M., Zhai, Z., Lu, X. & Luo, X. 2017 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
D’Yakov, S.P. 1954 Shock wave stability. Zh. Eksp. Teor. Fiz. 27, 288–295.Google Scholar
Freeman, N.C. 1955 A theory of the stability of plane shock waves. Proc. R. Soc. Lond. A 228, 341–362.Google Scholar
Fu, Z., Wang, C., Lin, Z., Zhu, G., Wang, K. & Luo, H. 2025 The impact of compressibility in Richtmyer–Meshkov instability. Phys. Plasmas 32, 022114.10.1063/5.0227404CrossRefGoogle Scholar
Groom, M. & Thornber, B. 2023 Numerical simulation of an idealised Richtmyer–Meshkov instability shock tube experiment. J. Fluid Mech. 964, A21.10.1017/jfm.2023.362CrossRefGoogle Scholar
Hu, S.X., Michel, D.T., Davis, A.K., Betti, R., Radha, P.B., Campbell, E.M., Froula, D.H. & Stoeckl, C. 2016 Understanding the effects of laser imprint on plastic-target implosions on OMEGA. Phys. Plasmas 23, 102701.10.1063/1.4962993CrossRefGoogle Scholar
Ishizaki, R., Nishihara, K., Sakagami, H. & Ueshima, Y. 1996 Instability of a contact surface driven by a nonuniform shock wave. Phys. Rev. E 53, R5592–R5595.10.1103/PhysRevE.53.R5592CrossRefGoogle ScholarPubMed
Jiang, G. & Shu, C. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228.10.1006/jcph.1996.0130CrossRefGoogle Scholar
Kane, J.O. et al. 2001 Interface imprinting by a rippled shock using an intense laser. Phys. Rev. E 63, 055401.10.1103/PhysRevE.63.055401CrossRefGoogle ScholarPubMed
Khokhlov, A.M., Oran, E.S., Chtchelkanova, A.Y. & Wheeler, J.C. 1999 Interaction of a shock with a sinusoidally perturbed flame. Combust. Flame 117 (1), 99–116.10.1016/S0010-2180(98)00090-XCrossRefGoogle 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
Li, J., Chen, C., Zhai, Z. & Luo, X. 2025 Asymptotic matching modal model on Richtmyer–Meshkov instability. J. Fluid Mech. 1002, A16.10.1017/jfm.2024.1125CrossRefGoogle Scholar
Li, J., Ding, J., Luo, X. & Zou, L. 2022 Instability of a heavy gas layer induced by a cylindrical convergent shock. Phys. Fluids 34, 042123.10.1063/5.0089845CrossRefGoogle Scholar
Liang, Y., Ding, J., Zhai, Z., Si, T. & Luo, X. 2017 Interaction of cylindrically converging diffracted shock with uniform interface. Phys. Fluids 29, 086101.10.1063/1.4997071CrossRefGoogle Scholar
Lindl, J., Landen, O., Edwards, J., Moses, E. & team, N.I.C. 2014 Review of the national ignition campaign 2009–2012. Phys. Plasmas 21, 020501.10.1063/1.4865400CrossRefGoogle Scholar
Lombardini, M., Hill, D.J., Pullin, D.I. & Meiron, DI. 2011 Atwood ratio dependence of Richtmyer–Meshkov flows under reshock conditions using large-eddy simulations. J. Fluid Mech. 670, 439–480.10.1017/S0022112010005367CrossRefGoogle Scholar
Lombardini, M. & Pullin, D.I. 2009 Startup process in the Richtmyer–Meshkov instability. Phys. Fluids 21, 044104.10.1063/1.3091943CrossRefGoogle 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
Meyer, K.A. & Blewett, P.J. 1972 Numerical investigation of the stability of a shock-accelerated interface between two fluids. Phys. Fluids 15, 753–759.10.1063/1.1693980CrossRefGoogle Scholar
Mikaelian, K.O. 1993 Effect of viscosity on Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Rev. E 47 (1), 375.10.1103/PhysRevE.47.375CrossRefGoogle ScholarPubMed
Napieralski, M., Cobos, F., Sánchez-Sanz, M. & Huete, C. 2024 Richtmyer–Meshkov instability when a shock wave encounters with a premixed flame from the burned gas. Appl. Math. Model. 134, 268–287.10.1016/j.apm.2024.05.041CrossRefGoogle Scholar
Niederhaus, C.E. & Jacobs, J.W. 2003 Experimental study of the Richtmyer–Meshkov instability of incompressible fluids. J. Fluid Mech. 485, 243–277.10.1017/S002211200300452XCrossRefGoogle Scholar
Nikolaev, I.M. 1965 Solution for a plane shock wave moving through a lightly curved interface of two media. J. Appl. Math. Mech. 29, 658–666.10.1016/0021-8928(65)90087-0CrossRefGoogle Scholar
Nishihara, K., Wouchuk, J., Matsuoka, C., Ishizaki, R. & Zhakhovsky, V. 2010 Richtmyer–Meshkov instability: theory of linear and nonlinear evolution. Phil. Trans. R. Soc. A 368, 1769–1807.10.1098/rsta.2009.0252CrossRefGoogle ScholarPubMed
Rayleigh, L. 1882 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 1, 170–177.10.1112/plms/s1-14.1.170CrossRefGoogle 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
Samtaney, R., Ray, J. & Zabusky, N.J. 1998 Baroclinic circulation generation on shock accelerated slow/fast gas interfaces. Phys. Fluids 10, 1214–1230.10.1063/1.869649CrossRefGoogle Scholar
Shen, N., Pullin, D.I., Samtaney, R. & Wheatley, V. 2021 Evolution of a shock generated by an impulsively accelerated, sinusoidal piston. J. Fluid Mech. 907, A35.10.1017/jfm.2020.775CrossRefGoogle Scholar
Tapinou, K.C., Wheatley, V., Bond, D. & Jahn, I. 2022 The Richtmyer–Meshkov instability of thermal, isotope and species interfaces in a five-moment multi-fluid plasma. J. Fluid Mech. 951, A11.10.1017/jfm.2022.847CrossRefGoogle 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
Wouchuk, J. & Nishihara, K. 1996 Linear perturbation growth at a shocked interface. Phys. Plasmas 3, 3761.10.1063/1.871940CrossRefGoogle Scholar
Wouchuk, J. & Nishihara, K. 1997 Asymptotic growth in the linear Richtmyer–Meshkov instability. Phys. Plasmas 4, 1028–1038.10.1063/1.872191CrossRefGoogle 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. 2025 Alternative analytical solution of linear Richtmyer–Meshkov-like flows for corrugated shocks driven by a rigid piston. Phys. Rev. E 111, 035102.10.1103/PhysRevE.111.035102CrossRefGoogle ScholarPubMed
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
Zaidel’, P.M. 1960 Shock wave from a slightly curved piston. J. Appl. Maths Mech. 24, 316–327.10.1016/0021-8928(60)90035-6CrossRefGoogle Scholar
Zhai, Z., Xu, J. & Luo, X. 2024 Convergent Richtmyer–Meshkov instability on two-dimensional tri-mode interfaces. Sci. China Phys. Mech. Astro. 67, 124711.10.1007/s11433-024-2471-7CrossRefGoogle Scholar
Zhai, Z., Zou, L., Wu, Q. & Luo, X. 2018 Review of experimental Richtmyer–Meshkov instability in shock tube: from simple to complex. Proc. Inst. Mech. Engrs C: J. Mech. Engng Sci. 232, 2830–2849.Google Scholar
Zhang, E., Liao, S., Zou, L., Zhai, Z., Liu, J. & Li, X. 2024 Refraction of a triple-shock configuration at planar fast–slow gas interfaces. J. Fluid Mech. 984, A49.10.1017/jfm.2024.245CrossRefGoogle Scholar
Zhang, Q. & Guo, W. 2016 Universality of finger growth in two-dimensional Rayleigh–Taylor and Richtmyer–Meshkov instabilities with all density ratios. J. Fluid Mech. 786, 47–61.10.1017/jfm.2015.641CrossRefGoogle Scholar
Zhang, W., Wu, Q., Zou, L., Zheng, X., Li, X., Luo, X. & Ding, J. 2018 Mach number effect on the instability of a planar interface subjected to a rippled shock. Phys. Rev. E 98, 043105.10.1103/PhysRevE.98.043105CrossRefGoogle Scholar
Zhang, Y., Zhao, Y., Ding, J. & Luo, X. 2023 Richtmyer–Meshkov instability with a rippled reshock. J. Fluid Mech. 968, A3.10.1017/jfm.2023.491CrossRefGoogle Scholar
Zhou, Y. 2017 Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720–722 1–136.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., Clark, T.T., Clark, D.S., Glendinning, S.G., Skinner, M.A., Huntington, C.M., Hurricane, O.A., Dimits, A.M. & Remington, B.A. 2019 Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities. Phys. Plasmas 26, 080901.10.1063/1.5088745CrossRefGoogle 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
Zou, L., Al-Marouf, M., Cheng, W., Samtaney, R., Ding, J. & Luo, X. 2019 Richtmyer–Meshkov instability of an unperturbed interface subjected to a diffracted convergent shock. J. Fluid Mech. 879, 448–467.10.1017/jfm.2019.694CrossRefGoogle Scholar
Zou, L., Liu, J., Liao, S., Zheng, X., Zhai, Z. & Luo, X. 2017 Richtmyer–Meshkov instability of a flat interface subjected to a rippled shock wave. Phys. Rev. E 95, 013107.10.1103/PhysRevE.95.013107CrossRefGoogle ScholarPubMed