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Shock-induced dual-layer evolution

Published online by Cambridge University Press:  02 November 2021

Yu Liang
NYUAD Research Institute, New York University Abu Dhabi, Abu Dhabi129188, UAE Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Xisheng Luo*
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Email address for correspondence:


Shock-induced fluid-layer evolution has attracted much attention but remains a challenge mainly because the coupling between layers remains unknown. Linear solutions are first derived to quantify the layer-coupling effect on the shocked dual-layer evolution. Next, the motions of the waves and interfaces of a dual layer are examined based on the one-dimensional gas dynamics theory. Shock-tube experiments on the dual-layer, single-layer and single-mode interface are then performed to validate the linear solutions and investigate the reverberating waves inside the layers. It is proved that the layer-coupling effect destabilises the dual layer, especially when the initial layers are thin, and the reverberating waves impose additional instabilities on all interfaces. Our findings suggest that a slow/fast configuration with a large thickness in a dual layer can facilitate the suppression of hydrodynamic instabilities.

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© The Author(s), 2021. Published by Cambridge University Press

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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, 6793.10.1017/jfm.2012.8CrossRefGoogle Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445468.10.1146/annurev.fluid.34.090101.162238CrossRefGoogle Scholar
Budzinski, J.M., Benjamin, R.F. & Jacobs, J.W. 1994 Influence of initial conditions on the flow patters of a shock-accelerated thin fluid layer. Phys. Fluids 6, 35103512.10.1063/1.868447CrossRefGoogle Scholar
Ding, J., Li, J., Sun, R., Zhai, Z. & Luo, X. 2019 Convergent Richtmyer–Meshkov instability of a heavy gas layer with perturbed outer interface. J. Fluid Mech. 878, 277291.10.1017/jfm.2019.661CrossRefGoogle Scholar
Drake, R.P. 2018 High-energy-density physics: foundation of inertial fusion and experimental astrophysics. Springer.10.1007/978-3-319-67711-8CrossRefGoogle Scholar
Goncharov, V.N. 1999 Theory of the ablative Richtmyer–Meshkov instability. Phys. Rev. Lett. 82 (10), 2091.10.1103/PhysRevLett.82.2091CrossRefGoogle Scholar
Guo, H.Y., Wang, L.F., Ye, W.H., Wu, J.F. & Zhang, W.Y. 2017 Linear growth of Rayleigh–Taylor instability of two finite-thickness fluid layers. Chin. Phys. Lett. 34 (7), 075201.CrossRefGoogle Scholar
Haines, B.M., et al. 2021 Constraining computational modeling of indirect drive double shell capsule implosions using experiments. Phys. Plasmas 28 (3), 032709.CrossRefGoogle 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 (6), R5592.10.1103/PhysRevE.53.R5592CrossRefGoogle ScholarPubMed
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, 2342.10.1017/S002211209500187XCrossRefGoogle Scholar
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, 583586.10.1103/PhysRevLett.70.583CrossRefGoogle ScholarPubMed
Kuranz, C.C., et al. 2018 How high energy fluxes may affect Rayleigh–Taylor instability growth in young supernova remnants. Nat. Commun. 9, 1564.10.1038/s41467-018-03548-7CrossRefGoogle ScholarPubMed
Liang, Y., Liu, L., Zhai, Z., Si, T. & Wen, C.-Y. 2020 Evolution of shock-accelerated heavy gas layer. J. Fluid Mech. 886, A7.10.1017/jfm.2019.1052CrossRefGoogle Scholar
Liang, Y. & Luo, X. 2021 On shock-induced heavy-fluid-layer evolution. J. Fluid Mech. 920, A13.10.1017/jfm.2021.438CrossRefGoogle Scholar
Liang, Y., Zhai, Z., Ding, J. & Luo, X. 2019 Richtmyer–Meshkov instability on a quasi-single-mode interface. J. Fluid Mech. 872, 729751.CrossRefGoogle Scholar
Lindl, J., Landen, O., Edwards, J., Moses, E. & Team, N. 2014 Review of the national ignition campaign 2009–2012. Phys. Plasmas 21, 020501.10.1063/1.4865400CrossRefGoogle Scholar
Liu, L., Liang, Y., Ding, J., Liu, N. & Luo, X. 2018 a An elaborate experiment on the single-mode Richtmyer–Meshkov instability. J. Fluid Mech. 853, R2.10.1017/jfm.2018.628CrossRefGoogle Scholar
Liu, W., Li, X., Yu, C., Fu, Y., Wang, P., Wang, L. & Ye, W. 2018 b Theoretical study on finite-thickness effect on harmonics in Richtmyer–Meshkov instability for arbitrary atwood numbers. Phys. Plasmas 25 (12), 122103.10.1063/1.5053766CrossRefGoogle Scholar
Meshkov, E.E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101104.CrossRefGoogle Scholar
Meyer, K.A. & Blewett, P.J. 1972 Numerical investigation of the stability of a shock-accelerated interface between two fluids. Phys. Fluids 15, 753759.CrossRefGoogle Scholar
Mikaelian, K.O. 1985 Richtmyer–Meshkov instabilities in stratified fluids. Phys. Rev. A 31, 410419.10.1103/PhysRevA.31.410CrossRefGoogle ScholarPubMed
Mikaelian, K.O. 1993 Growth rate of the Richtmyer–Meshkov instability at shocked interfaces. Phys. Rev. Lett. 71 (18), 2903.CrossRefGoogle ScholarPubMed
Mikaelian, K.O. 1996 Numerical simulations of Richtmyer–Meshkov instabilities in finite-thickness fluid layers. Phys. Fluids 8 (5), 12691292.CrossRefGoogle Scholar
Miles, A.R., Edwards, M.J., Blue, B., Hansen, J.F., Robey, H.F., Drake, R.P., Kuranz, C. & Leibrandt, D.R. 2004 The effects of a short-wavelength mode on the evolution of a long-wavelength perturbatoin driven by a strong blast wave. Phys. Plasmas 11, 55075519.CrossRefGoogle Scholar
Montgomery, D.S., et al. 2018 Design considerations for indirectly driven double shell capsules. Phys. Plasmas 25 (9), 092706.CrossRefGoogle Scholar
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), 114101.10.1063/1.4827435CrossRefGoogle Scholar
Ott, E. 1972 Nonlinear evolution of the Rayleigh–Taylor instability of a thin layer. Phys. Rev. Lett. 29 (21), 1429.CrossRefGoogle Scholar
Prestridge, K., Vorobieff, P., Rightley, P.M. & Benjamin, R.F. 2000 Validation of an instability growth model using particle image velocimetry measurement. Phys. Rev. Lett. 84, 43534356.10.1103/PhysRevLett.84.4353CrossRefGoogle Scholar
Qiao, X. & Lan, K. 2021 Novel target designs to mitigate hydrodynamic instabilities growth in inertial confinement fusion. Phys. Rev. Lett. 126 (18), 185001.10.1103/PhysRevLett.126.185001CrossRefGoogle ScholarPubMed
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. London Math. Soc. 14, 170177.Google Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297319.CrossRefGoogle Scholar
Rightley, P.M., Vorobieff, P. & Benjamin, R.F. 1997 Evolution of a shock-accelerated thin fluid layer. Phys. Fluids 9 (6), 17701782.CrossRefGoogle Scholar
Sharp, D.H. 1984 An overview of Rayleigh–Taylor instability. Physica D 12 (1), 318.10.1016/0167-2789(84)90510-4CrossRefGoogle Scholar
Sun, R., Ding, J., Zhai, Z., Si, T. & Luo, X. 2020 Convergent Richtmyer–Meshkov instability of heavy gas layer with perturbed inner surface. J. Fluid Mech. 902, A3.CrossRefGoogle 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 (1065), 192196.Google Scholar
Tomkins, C., Kumar, S., Orlicz, G. & Prestridge, K. 2008 An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech. 611, 131150.10.1017/S0022112008002723CrossRefGoogle 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. Eng. C 232, 28302849.CrossRefGoogle Scholar
Zhou, Y. 2017 a Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720-722, 1136.Google Scholar
Zhou, Y. 2017 b Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723–725, 1160.Google Scholar
Zhou, Y., Clark, T.T., Clark, D.S., Glendinning, S.S., Skinner, A.A., Huntington, C., Hurricane, O.A., Dimits, A.M. & Remington, B.A. 2019 Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities. Phys. Plasmas 26 (8), 080901.10.1063/1.5088745CrossRefGoogle Scholar
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