Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-09T14:49:08.544Z Has data issue: false hasContentIssue false
  • English
  • Français

Mechanism and modelling of the secondary baroclinic vorticity in the Richtmyer–Meshkov instability

Published online by Cambridge University Press:  02 February 2021

Naifu Peng Open the ORCID record for Naifu Peng [Opens in a new window] ,
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window] ,
Jinxin Wu Open the ORCID record for Jinxin Wu [Opens in a new window]  and
Zuoli Xiao Open the ORCID record for Zuoli Xiao [Opens in a new window]
Naifu Peng
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China Center for Applied Physics and Technology and HEDPS, Peking University, Beijing100871, PR China
Yue Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China Center for Applied Physics and Technology and HEDPS, Peking University, Beijing100871, PR China Beijing Innovation Center for Engineering Science and Advanced Technology, Peking University, Beijing100871, PR China
Jinxin Wu
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China
Zuoli Xiao
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China Center for Applied Physics and Technology and HEDPS, Peking University, Beijing100871, PR China Beijing Innovation Center for Engineering Science and Advanced Technology, Peking University, Beijing100871, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We elucidate the effect of the secondary baroclinic vorticity (SBV) on the Richtmyer–Meshkov instability (RMI) accelerated by a weak incident shock and develop a vortex-based model for spike and bubble growth rates. Two major mechanisms of the single-mode RMI, the primary baroclinic vorticity (PBV) and the pressure perturbation, are distinguished by simplified models with the vortex-surface field. We find that the effect of the pressure perturbation can be neglected in the present RMI, and the growth of the interface or vortex surface is first driven by the PBV. Subsequently, the SBV, generated by the misalignment between the density gradient across the interface and the pressure gradient produced by the PBV-induced velocity, leads to the nonlinear growth of the interface with the generation of spikes and bubbles. Inspired by this mechanism, we develop a predictive model of spike and bubble growth rates using the motion of viscous vortex rings. The circulation of the vortex ring is modelled with the SBV effect. This model is validated by five data sets of direct numerical simulations and experiments of the single-mode RMI with various initial conditions.

JFM classification

Vortex Flows: Vortex dynamics Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A56
Check for updates
Copyright
© The Author(s), 2021. 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.)

References

REFERENCES

Aglitskiy, Y., et al. . 2010 Basic hydrodynamics of Richtmyer–Meshkov-type growth and oscillations in the inertial confinement fusion-relevant conditions. Phil. Trans. R. Soc. Lond. A 368, 1739–1768.Google ScholarPubMed
Almgren, A.S., Bell, J.B., Rendleman, C.A. & Zingale, M. 2006 Low Mach number modeling of type Ia supernovae. I. Hydrodyn. Astrophys. J. 637, 922–936.CrossRefGoogle Scholar
Alon, U., Hecht, J., Ofer, D. & Shvarts, D. 1995 Power laws and similarity of Rayleigh–Taylor and Richtmyer–Meshkov mixing fronts at all density ratios. Phys. Rev. Lett. 74, 534.CrossRefGoogle ScholarPubMed
Arnett, D. 2000 The role of mixing in astrophysics. Astrophy. J. Suppl. 127, 213.CrossRefGoogle Scholar
Arnett, W.D., Bahcall, J.N., Kirshner, R.P. & Woosley, S.E. 1989 Supernova 1987A. Annu. Rev. Astron. Astrophys. 27, 629–700.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Carlès, P. & Popinet, S. 2002 The effect of viscosity, surface tension and non-linearity on Richtmyer–Meshkov instability. Eur. J. Mech. B/Fluids 21, 511–526.CrossRefGoogle Scholar
Chapman, S. & Cowling, T.G. 1990 The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity. Cambridge University Press.Google Scholar
Chapman, P.R. & Jacobs, J.W. 2006 Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys. Fluids 18, 074101.CrossRefGoogle Scholar
Cook, A.W. 2009 Enthalpy diffusion in multicomponent flows. Phys. Fluids 21, 055109.CrossRefGoogle Scholar
Courant, R. & Friedrichs, K.O. 1999 Supersonic Flow and Shock Waves. Springer.Google Scholar
Dimonte, G. & Ramaprabhu, P. 2010 Simulations and model of the nonlinear Richtmyer–Meshkov instability. Phys. Fluids 22, 014104.CrossRefGoogle Scholar
Evans, L.C. 1998 Partial Differential Equations. American Mathematical Society.Google Scholar
Fraley, G. 1986 Rayleigh–Taylor stability for a normal shock wave-density discontinuity interaction. Phys. Fluids 29, 376–386.CrossRefGoogle Scholar
Fukumoto, Y. & Kaplanski, F. 2008 Global time evolution of an axisymmetric vortex ring at low Reynolds numbers. Phys. Fluids 20, 053103.CrossRefGoogle Scholar
Fukumoto, Y. & Moffatt, H.K. 2008 Kinematic variational principle for motion of vortex rings. Physica D 237, 2210–2217.CrossRefGoogle Scholar
Goncharov, V.N. 1999 Theory of the ablative Richtmyer–Meshkov instability. Phys. Rev. Lett. 82, 2091.CrossRefGoogle Scholar
Gottlieb, S. & Shu, C.-W. 1998 Total variation diminishing Runge–Kutta schemes. Maths Comput. 67, 73–85.CrossRefGoogle Scholar
Graves, R.E. & Argrow, B.M. 1999 Bulk viscosity: past to present. J. Thermophys. Heat Transfer 13, 337–342.CrossRefGoogle Scholar
Gupta, S., Zhang, S. & Zabusky, N.J. 2003 Shock interaction with a heavy gas cylinder: emergence of vortex bilayers and vortex-accelerated baroclinic circulation generation. Laser Part. Beams 21, 443–448.CrossRefGoogle Scholar
Haan, S.W. 1991 Weakly nonlinear hydrodynamic instabilities in inertial fusion. Phys. Fluids B 3, 2349–2355.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Hao, J., Xiong, S. & Yang, Y. 2019 Tracking vortex surfaces frozen in the virtual velocity in non-ideal flows. J. Fluid Mech. 863, 513–544.CrossRefGoogle Scholar
Hill, D.J., Pantano, C. & Pullin, D.I. 2006 Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock. J. Fluid Mech. 557, 29–61.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, R5592.CrossRefGoogle ScholarPubMed
Jacobs, J.W. & Krivets, V.V. 2005 Experiments on the late-time development of single-mode Richtmyer–Meshkov instability. Phys. Fluids 17, 034105.CrossRefGoogle Scholar
Jacobs, J.W. & Sheeley, J.M. 1996 Experimental study of incompressible Richtmyer–Meshkov instability. Phys. Fluids 8, 405–415.CrossRefGoogle Scholar
Jiang, G.S. & Shu, C.-W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228.CrossRefGoogle Scholar
Kawai, S. & Lele, S.K. 2008 Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes. J. Comput. Phys. 227, 9498–9526.CrossRefGoogle Scholar
Khokhlov, A.M., Oran, E.S. & Thomas, G.O. 1999 Numerical simulation of deflagration-to-detonation transition: the role of shock-flame interactions in turbulent flames. Combust. Flame 117, 323–339.CrossRefGoogle Scholar
Kokkinakis, I.W., Drikakis, D. & Youngs, D.L. 2019 Modeling of Rayleigh–Taylor mixing using single-fluid models. Phys. Rev. E 99, 013104.CrossRefGoogle ScholarPubMed
Kotelnikov, A.D., Ray, J. & Zabusky, N.J. 2000 Vortex morphologies on reaccelerated interfaces: visualization, quantification and modeling of one-and two-mode compressible and incompressible environments. Phys. Fluids 12, 3245–3264.CrossRefGoogle Scholar
Latini, M., Schilling, O. & Don, W.S. 2007 High-resolution simulations and modeling of reshocked single-mode Richtmyer–Meshkov instability: comparison to experimental data and to amplitude growth model predictions. Phys. Fluids 19, 024104.CrossRefGoogle Scholar
Liang, Y., Zhai, Z., Ding, J. & Luo, X. 2019 Richtmyer–Meshkov instability on a quasi-single-mode interface. J. Fluid Mech. 872, 729–751.CrossRefGoogle Scholar
Likhachev, O.A. & Jacobs, J.W. 2005 A vortex model for Richtmyer–Meshkov instability accounting for finite Atwood number. Phys. Fluids 17, 031704.CrossRefGoogle 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.CrossRefGoogle Scholar
Liu, H. & Xiao, Z. 2016 Scale-to-scale energy transfer in mixing flow induced by the Richtmyer–Meshkov instability. Phys. Rev. E 93, 053112.CrossRefGoogle ScholarPubMed
Lombardini, M. & Pullin, D.I. 2009 Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability. Phys. Fluids 21, 114103.CrossRefGoogle Scholar
Long, C.C., Krivets, V.V., Greenough, J.A. & Jacobs, J.W. 2009 Shock tube experiments and numerical simulation of the single-mode, three-dimensional Richtmyer–Meshkov instability. Phys. Fluids 21, 114104.CrossRefGoogle Scholar
Luo, X., Wang, X. & Si, T. 2013 The Richtmyer–Meshkov instability of a three-dimensional air/$\textrm {SF}_6$ interface with a minimum-surface feature. J. Fluid Mech. 722, R2.CrossRefGoogle Scholar
Meiron, D. & Meloon, M. 1997 Richtmyer–Meshkov instability in compressible stratified fluids. In Proceedings of the 6th International Workshop on the Physics of Compressible Turbulent Mixing, Marseille, France (ed. G. Jourdan & L. Hovas), pp. 337–342. Institut Universitaire Thermiques Industriels, Marseille, France.Google Scholar
Meshkov, E.E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.CrossRefGoogle Scholar
Mikaelian, K.O. 1993 Effect of viscosity on Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Rev. E 47, 375.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Morgan, R.V., Aure, R., Stockero, J.D., Greenough, J.A., Cabot, W., Likhachev, O.A. & Jacobs, J.W. 2012 On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments. J. Fluid Mech. 712, 354–383.CrossRefGoogle Scholar
Movahed, P. & Johnsen, E. 2013 A solution-adaptive method for efficient compressible multifluid simulations, with application to the Richtmyer–Meshkov instability. J. Comput. Phys. 239, 166–186.CrossRefGoogle Scholar
Niederhaus, C.E. & Jacobs, J.W. 2003 Experimental study of the Richtmyer–Meshkov instability of incompressible fluids. J. Fluid Mech. 485, 243–277.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Oggian, T., Drikakis, D., Youngs, D.L. & Williams, R.J.R. 2015 Computing multi-mode shock-induced compressible turbulent mixing at late times. J. Fluid Mech. 779, 411–431.CrossRefGoogle Scholar
Olson, B.J. & Lele, S.K. 2013 A mechanism for unsteady separation in over-expanded nozzle flow. Phys. Fluids 25, 239–249.CrossRefGoogle Scholar
Ortega, A., Hill, D.J., Pullin, D.I. & Meiron, D.I. 2010 Linearized Richtmyer–Meshkov flow analysis for impulsively accelerated incompressible solids. Phys. Rev. E 81, 066305.CrossRefGoogle Scholar
Pantano, C., Deiterding, R., Hill, D.J. & Pullin, D.I. 2007 A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows. J. Comput. Phys. 221, 63–87.CrossRefGoogle Scholar
Peng, N. & Yang, Y. 2018 Effects of the Mach number on the evolution of vortex-surface fields in compressible Taylor–Green flows. Phys. Rev. Fluids 3, 013401.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Ramshaw, J.D. 1990 Self-consistent effective binary diffusion in multicomponent gas mixtures. J. Non-Equilib. Thermodyn. 15, 295–300.CrossRefGoogle Scholar
Rasmus, A.M., et al. . 2018 Shock-driven discrete vortex evolution on a high-Atwood number oblique interface. Phys. Plasma 25, 032119.CrossRefGoogle Scholar
Reid, R.C., Pransuitz, J.M. & Poling, B.E. 1987 The Properties of Gases and Liquids. McGraw-Hill.Google Scholar
Reinaud, J., Joly, L. & Chassaing, P. 2000 The baroclinic secondary instability of the two-dimensional shear layer. Phys. Fluids 12, 2489–2505.CrossRefGoogle Scholar
Richtmyer, R.D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.CrossRefGoogle Scholar
Sadot, O., Erez, L., Alon, U., Oron, D., Levin, L.A., Erez, G., Ben-Dor, G. & Shvarts, D. 1998 Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer–Meshkov instability. Phys. Rev. Lett. 80, 1654.CrossRefGoogle Scholar
Saffman, P.G. 1970 The velocity of viscous vortex rings. Stud. Appl. Maths 49, 371–380.CrossRefGoogle Scholar
Samtaney, R., Ray, J. & Zabusky, N.J. 1998 Baroclinic circulation generation on shock accelerated slow/fast gas interfaces. Phys. Fluids 10, 1217–1230.CrossRefGoogle Scholar
Samtaney, R. & Zabusky, N.J. 1994 Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws. J. Fluid Mech. 269, 45–78.CrossRefGoogle Scholar
Shankar, S.K., Kawai, S. & Lele, S.K. 2011 Two-dimensional viscous flow simulation of a shock accelerated heavy gas cylinder. Phys. Fluids 23, 131.CrossRefGoogle Scholar
Sohn, S.-I. 2004 Vortex model and simulations for Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Rev. E 69, 036703.CrossRefGoogle ScholarPubMed
Sohn, S.-I. 2009 Effects of surface tension and viscosity on the growth rates of Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Rev. E 80, 055302.CrossRefGoogle ScholarPubMed
Soteriou, M.C. & Ghoniem, A.F. 1995 Effects of the free-stream density ratio on free and forced spatially developing shear layers. Phys. Fluids 7, 2036–2051.CrossRefGoogle Scholar
Staquet, C. 1995 Two-dimensional secondary instabilities in a strongly stratified shear layer. J. Fluid Mech. 296, 73–126.CrossRefGoogle Scholar
Taccetti, J.M., Batha, S.H., Fincke, J.R., Delamater, N.D., Lanier, N.E., Magelssen, G.R., Hueckstaedt, R.M., Rothman, S.D., Horsfield, C.J. & Parker, K.W. 2005 Richtmyer–Meshkov instability reshock experiments using laser-driven double-cylinder implosions. Astrophys. Space Sci. 298, 327–331.CrossRefGoogle Scholar
Thornber, B., Drikakis, D., Youngs, D.L. & Williams, R.J.R. 2010 The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability. J. Fluid Mech. 654, 99–139.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Thornber, B., Drikakis, D., Youngs, D.L. & Williams, R.J.R. 2012 Physics of the single-shocked and reshocked Richtmyer–Meshkov instability. J. Turbul. 13, 1–17.CrossRefGoogle Scholar
Tritschler, V.K., Zubel, M., Hickel, S. & Adams, N.A. 2014 Evolution of length scales and statistics of Richtmyer–Meshkov instability from direct numerical simulations. Phys. Rev. E 90, 063001.CrossRefGoogle ScholarPubMed
Tung, C. & Ting, L. 1967 Motion and decay of a vortex ring. Phys. Fluids 10, 901–910.CrossRefGoogle Scholar
Vandenboomgaerde, M., Gauthier, S. & Mügler, C. 2002 Nonlinear regime of a multimode Richtmyer–Meshkov instability: a simplified perturbation theory. Phys. Fluids 14, 1111–1122.CrossRefGoogle Scholar
Velikovich, A.L., Dahlburg, J.P., Schmitt, A.J., Gardner, J.H., Phillips, L., Cochran, F.L., Chong, Y.K., Dimonte, G. & Metzler, N. 2000 Richtmyer–Meshkov-like instabilities and early-time perturbation growth in laser targets and Z-pinch loads. Phys. Plasmas 7, 1662–1671.CrossRefGoogle Scholar
Velikovich, A.L., Herrmann, M. & Abarzhi, S.I. 2014 Perturbation theory and numerical modelling of weakly and moderately nonlinear dynamics of the incompressible Richtmyer–Meshkov instability. J. Fluid Mech. 751, 432–479.CrossRefGoogle Scholar
Vorobieff, P., Tomkins, C., Kumar, S., Goodenough, C., Mohamed, N.G. & Benjamin, R.F. 2004 Secondary instabilities in shock-induced transition to turbulence. Adv. Fluid Mech. 45, 139–148.Google Scholar
Wouchuk, J.G. 2001 Growth rate of the linear Richtmyer–Meshkov instability when a shock is reflected. Phys. Rev. E 63, 056303.CrossRefGoogle ScholarPubMed
Wouchuk, J.G. & Nishihara, K. 1997 Asymptotic growth in the linear Richtmyer–Meshkov instability. Phys. Plasmas 4, 1028–1038.CrossRefGoogle Scholar
Wu, J., Liu, H. & Xiao, Z. 2019 A numerical investigation of Richtmyer–Meshkov instability in spherical geometry. Adv. Appl. Maths Mech. 11, 583–597.CrossRefGoogle Scholar
Xiong, S. & Yang, Y. 2019 a Construction of knotted vortex tubes with the writhe-dependent helicity. Phys. Fluids 31, 047101.CrossRefGoogle Scholar
Xiong, S. & Yang, Y. 2019 b Identifying the tangle of vortex tubes in homogeneous isotropic turbulence. J. Fluid Mech. 874, 952–978.CrossRefGoogle Scholar
Yang, J., Kubota, T. & Zukoski, E.E. 1993 Applications of shock-induced mixing to supersonic combustion. AIAA J. 31, 854–862.CrossRefGoogle Scholar
Yang, Y. & Pullin, D.I. 2010 On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions. J. Fluid Mech. 661, 446–481.CrossRefGoogle Scholar
Yang, Y. & Pullin, D.I. 2011 Evolution of vortex-surface fields in viscous Taylor–Green and Kida–Pelz flows. J. Fluid Mech. 685, 146–164.CrossRefGoogle Scholar
Yang, Y., Zhang, Q. & Sharp, D.H. 1994 Small amplitude theory of Richtmyer–Meshkov instability. Phys. Fluids 6, 1856–1873.CrossRefGoogle Scholar
Zabusky, N.J. 1999 Vortex paradigm for accelerated inhomogeneous flows: visiometrics for the Rayleigh–Taylor and Richtmyer–Meshkov environments. Annu. Rev. Fluid Mech. 31, 495–536.CrossRefGoogle Scholar
Zabusky, N.J., Kotelnikov, A.D., Gulak, Y. & Peng, G. 2003 Amplitude growth rate of a Richtmyer–Meshkov unstable two-dimensional interface to intermediate times. J. Fluid Mech. 475, 147–162.CrossRefGoogle Scholar
Zabusky, N.J. & Zeng, S.M. 1998 Shock cavity implosion morphologies and vortical projectile generation in axisymmetric shock-spherical fast/slow bubble interactions. J. Fluid Mech. 362, 327–346.CrossRefGoogle Scholar
Zabusky, N.J. & Zhang, S. 2002 Shock-planar curtain interactions in two dimensions: emergence of vortex double layers, vortex projectiles, and decaying stratified turbulence. Phys. Fluids 14, 419–422.CrossRefGoogle Scholar
Zaidel, P.M. 1960 Shock wave from a slightly curved piston. Z. Angew. Math. Mech. 24, 316–327.CrossRefGoogle Scholar
Zhang, S., Peng, G. & Zabusky, N.J. 2005 Vortex dynamics and baroclinically forced inhomogeneous turbulence for shock-planar heavy curtain interactions. J. Turbul. 6, N3.CrossRefGoogle Scholar
Zhang, Q. & Sohn, S.-I. 1996 An analytical nonlinear theory of Richtmyer–Meshkov instability. Phys. Lett. A 212, 149–155.CrossRefGoogle Scholar
Zhang, Q. & Sohn, S.-I. 1997 Nonlinear theory of unstable fluid mixing driven by shock wave. Phys. Fluids 9, 1106–1124.CrossRefGoogle Scholar
Zhang, Q. & Sohn, S.-I. 1999 Quantitative theory of Richtmyer–Meshkov instability in three dimensions. Z. Angew. Math. Phys. 50, 1–46.CrossRefGoogle Scholar
Zhang, S. & Zabusky, N.J. 2003 Shock-planar curtain interactions: strong secondary baroclinic deposition and emergence of vortex projectiles and late-time inhomogeneous turbulence. Laser Part. Beams 21, 463–470.CrossRefGoogle Scholar
Zhang, S., Zabusky, N.J., Peng, G. & Gupta, S. 2004 Shock gaseous cylinder interactions: dynamically validated initial conditions provide excellent agreement between experiments and numerical simulations to late-intermediate time. Phys. Fluids 16, 1203–1216.CrossRefGoogle Scholar
Zhao, Y., Xiong, S., Yang, Y. & Chen, S. 2018 Sinuous distortion of vortex surfaces in the lateral growth of turbulent spots. Phys. Rev. Fluids 3, 074701.CrossRefGoogle Scholar
Zhao, Y., Yang, Y. & Chen, S. 2016 Vortex reconnection in the late transition in channel flow. J. Fluid Mech. 802, R4.CrossRefGoogle Scholar
Zhou, Y. 2001 A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Fluids 13, 538–543.CrossRefGoogle Scholar
Zhou, Y. 2017 a Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720a, 1–136.Google Scholar
Zhou, Y. 2017 b Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys. Rep. 723, 1–160.Google Scholar
Zhou, H., You, J., Xiong, S., Yang, Y., Thévenin, D. & Chen, S. 2019 Interactions between the premixed flame front and the three-dimensional Taylor–Green vortex. Proc. Combust. Inst. 37, 2461–2468.CrossRefGoogle Scholar