Richtmyer-Meshkov instability: Theory of linear and nonlinear evolution

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 368, Issue 1916, 2010, Pages 1769-1807

  Nishihara, K ^a   Wouchuk, J G ^b   Matsuoka, C ^c   Ishizaki, R ^d   Zhakhovsky, V V ^a,e  

^a OSAKA UNIVERSITY   (Japan)

^b UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

^c EHIME UNIVERSITY   (Japan)

^d NATIONAL INSTITUTE FOR FUSION SCIENCE   (Japan)

^e UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

Laser fusion; Nonlinear hydrodynamics; Richtmyer meshkov instability; Shock wave; Vortex sheet; Vorticity

Indexed keywords

ASYMPTOTIC ANALYSIS; COMPUTER SIMULATION; CORRUGATED MATERIALS; FLUID DYNAMICS; HYDRODYNAMICS; LASER FUSION; LASER RADIATION; MODELS; MOLECULAR DYNAMICS; PHASE INTERFACES; SHOCK WAVES; STABILITY; UNDERWATER ACOUSTICS; VELOCITY; VORTICITY; WAVEFRONTS;

ANALYTICAL MODEL; CONTACT SURFACE; CYLINDRICAL GEOMETRY; EXTERNAL SOURCES; GOVERNING PARAMETERS; INCIDENT SHOCK; INSTABILITY GROWTH; IRROTATIONAL; LINEAR GROWTH RATE; MATERIAL BOUNDARIES; MATERIAL INTERFACES; MOLECULAR DYNAMICS SIMULATIONS; NON-LINEAR HYDRODYNAMICS; NONLINEAR EVOLUTIONS; NONLINEAR PHASE; NONUNIFORM; PERTURBATION WAVELENGTH; PRESSURE PERTURBATION; RICHTMYER MESHKOV INSTABILITY; RIPPLE AMPLITUDES; SHOCK FRONTS; SOUND WAVES; STABILIZATION MECHANISMS; THEORETICAL FRAMEWORK; TWO-FLUID; VORTEX SHEET;

SURFACES;

EID: 77950940295     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2009.0252     Document Type: Article

References (105)

1. Abarzhi, S. I. 2002 Nonlinear evolution of unstable fluid interface. Phys. Rev. E. 66, 0 036 301.
2. Abarzhi, S. I. 2008 Review of nonlinear dynamics of the unstable fluid interface: conservation laws and group theory. Phys. Scr. T 132, 014 012.
3. Abarzhi, S. I., Nishihara, K. & Glimm, J. 2003 Rayleigh-Taylor and Richtmyer-Meshkov instabilities for fluids with a finite density ratio. Phys. Lett. A 317, 470-476. (doi:10.1016/ j.physleta.2003.09.013)
4. Abéguilé, F., Boudesocque-Dubois, C., Clarisse, J.-M., Gauthier, S. & Saillard, Y. 2006 Linear perturbation amplification in self-similar ablation flows of inertial confinement fusion. Phys. Rev. Lett. 97, 035 002. (Pubitemid 44100053)
5. Aglitskiy, Y. et al. 2001 Direct observation of mass oscillations due to ablative Richtmyer-Meshkov instability in plastic targets. Phys. Rev. Lett. 87, 265 001. (Pubitemid 34047346)
6. Aglitskiy, Y. et al. 2002 Direct observation of oscillations due to ablative Richtmyer- Meshkov instability and feedout in planar plastic target. Phys. Plasmas 9, 2264-2276. (doi:10.1063/1.1459459)
7. Andreopoulos, Y., Agui, J. H. & Briassulis, G. 2000 Shock-wave turbulence interactions. Annu. Rev. Fluid Mech. 32, 309-345. (doi:10.1146/annurev.fluid.32.1.309) (Pubitemid 36144999)
8. Azechi, H. et al. 1997 Direct-drive hydrodynamic instability experiments on the GEKKO XII laser. Phys. Plasmas 4, 4079-4089. (doi:10.1063/1.872528) (Pubitemid 127639072)
9. Baker, G. A. & P. Graves-Morris. 1981 Padé approximants. Reading, MA: Addison-Wesley.
10. Baker, G. R., Meiron, D. I. & Orszag, S. A. 1982 Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477-501. (doi:10.1017/S0022112082003164) (Pubitemid 13477070)
11. Bates, J. W. & Montgomery, C. 2000 The D'yakov-Kontorovich instability of shock waves in real gases. Phys. Rev. Lett. 84, 1180-1183. (doi:10.1103/PhysRevLett.84.1180)
12. Birkhoff, G. 1962 Helmholtz and Taylor instability. Proc. Symp. Appl. Math. 13, 55.
13. Bobin, J. L. 1971 Flame propagation and overdense heating in a laser created plasma. Phys. Fluids 14, 2341-2354.
14. Briscoe, M. G. & Kovitz, A. A. 1968 Instability of a contact surface driven by a nonuniform shock wave. J. Fluid Mech. 31, 529-546. (doi:10.1017/S0022112068000315)
15. Brouillette, M. 2002 The Richtmyer-Meshkov instability. Annu. Rev. Fluid Mech. 34, 445-468. (doi:10.1146/annurev.fluid.34.090101.162238) (Pubitemid 35372030)
16. Carles, P. & Popinet, S. 2001 Viscous non linear theory of Richtmyer-Meshkov instability. Phys. Fluids 13, 1833-1836.
17. Clarisse, J.-M., Boudesocque-Dubois, C. & Gauthier, S. 2008 Linear perturbation response of self-similar ablative flows relevant to inertial confinement fusion. J. Fluid Mech. 609, 1-48. (doi:10.1017/S0022112008002279)
18. Desselberger, M., Jones, M. W., Edwards, J., Dunne, M. & Willi, O. 1995 Use of X-ray preheated foam layers to reduce beam structure imprint in laser-driven targets. Phys. Rev. Lett. 74, 2961-2964.
19. Dimonte, G., Frerking, C. E., Schneider, M. & Remington, B. 1996 Richtmyer-Meshkov instability with strong radiatively driven shocks. Phys. Plasmas 3, 614-630. (doi:10.1063/1.871889) (Pubitemid 126609319)
20. D'yakov, S. P. 1955 On the stability of shock waves. Zh. Eksp. Teor. Fiz. 27, 288-294.
21. Emery, M. H., Gardner, J. H., Lehmberg, R. H. & Obenschain, S. P. 1991 Hydrodynamic target response to an induced spatial incoherence-smoothed laser beam. Phys. Fluids 79, 2640-2651.
22. Endo, T. et al. 1995 Dynamic behavior of rippled shock waves and subsequently induced areal-density-perturbation growth in laser-irradiated foils. Phys. Rev. Lett. 74, 3608-3611. (doi:10.1103/PhysRevLett.74.3608)
23. Fraley, G. 1986 Rayleigh-Taylor stability for a normal shock wave-density discontinuity interaction. Phys. Fluids 29, 376-387. (doi:10.1063/1.865722)
24. Germann, T. C., Hammerberg, J. E. & Holian, B. L. 2004 Large-scale molecular dynamics simulations of ejecta formation in copper. In Proc. Conf. American Physical Society Topical Group on Shock Compression of Condensed Matter, Portland, OR, 20-25 July 2003, vol.706, pp. 285-288. Melville, NY: American Institute of Physics.
25. Glosli, J. N., Caspersen, K. J., Gunnels, J. A., Richards, D. F., Rudd, R. E. & Streitz, F. H. 2007 Extending stability beyond CPU millennium: a micron-scale atomistic simulation of Kelvin- Helmholtz instability. In Proc. 2007 ACM/IEEE Conf. on Supercomputing, Reno, NV, 10-16 November 2007, article 58. New York, NY: ACM.
26. Goncharov, V. N. 1999 Theory of the ablative Richtmyer-Meshkov instability. Phys. Rev. Lett. 82, 2091-2094. (doi:10.1103/PhysRevLett.82.2091)
27. Goncharov, V. N. et al. 2000 A model of laser imprinting. Phys. Plasmas 7, 2062-2068. (doi:10.1063/1.874028)
28. Goncharov, V. N. et al. 2006 Early stage of implosion in inertial confinement fusion: shock timing and perturbation evolution. Phys. Plasmas 13, 012 702.
29. Gotchev, O. V., Goncharov, V. N., Knauer, J. P., Boehly, T. R., Collins, T. J. B., Epstein, R., Jaanimagi, P. A. & Meyerhofer, D. D. 2006 Test of thermal transport models through dynamic overpressure stabilization of ablation-front perturbation growth in laser-driven CH foils. Phys. Rev. Lett. 96, 115 005.
30. Griffond, J. 2005 Linear interaction analysis applied to a mixture of two perfect gases. Phys. Fluids 17, 086 101. (Pubitemid 41226585)
31. Griffond, J. 2006 Linear interaction analysis for Richtmyer-Meshkov instability at low Atwood numbers. Phys. Fluids 18, 054 106. (Pubitemid 43833769)
32. Hawley, J. F. & Zabusky, N. J. 1989 Vortex paradigm for shock-accelerated density-stratified interfaces. Phys. Rev. Lett. 63, 1241-1244. (doi:10.1103/PhysRevLett.63.1241)
33. Herrmann, M., Moin, P. & Abarzhi, S. I. 2008 Nonlinear evolution of the Richtmyer-Meshkov instability. J. Fluid. Mech. 612, 311-338. (doi:10.1017/S0022112008002905)
34. Holmes, R. L. et al. 1999 Richtmyer-Meshkov instability growth: experiment, simulation and theory. J. Fluid Mech. 389, 55-79. (doi:10.1017/S0022112099004838)
35. Houas, L. & Chemouni, I. 1996 Experimental investigation of Richtmyer-Meshkov instability in shock tube. Phys. Fluids 8, 614-627. (doi:10.1063/1.868845) (Pubitemid 126609176)
36. Ishizaki, R. & Nishihara, K. 1997 Propagation of a rippled shock wave driven by nonuniform laser ablation. Phys. Rev. Lett. 78, 1920-1923. (doi:10.1103/PhysRevLett.78.1920) (Pubitemid 127647393)
37. Ishizaki, R. & Nishihara, K. 1998 Model of hydrodynamic perturbation growth in the start-up phase of laser implosion. Phys. Rev. E 58, 3744-3767. (doi:10.1103/PhysRevE.58.3744) (Pubitemid 128603413)
38. 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. (doi:10.1103/PhysRevE.53.R5592)
39. Jacobs, J. W. & Sheeley, J. M. 1996 Experimental study of incompressible Richtmyer-Meshkov instability. Phys. Fluids 8, 405-415. (doi:10.1063/1.868794) (Pubitemid 126609157)
40. Jones, M. A. & Jacobs, J. W. 1997 A membraneless experiment for the study of Richtmyer- Meshkov instability of a shock-accelerated gas interface. Phys. Fluids 9, 3078-3085. (doi:10.1063/1.869416) (Pubitemid 27520486)
41. Kadau, K., Germann, T. C., Hadjiconstantinou, N. G., Lomdahl, P. S., Dimonte, G., Holian, B. L. & Alder, B. J. 2004 Nanohydrodynamics simulations: an atomistic view of the Rayleigh-Taylor instability. Proc. Natl Acad. Sci. USA 101, 5851-5855. (doi:10.1073/pnas.0401228101) (Pubitemid 38520491)
42. Kadau, K., Barber, J. L., Germann, T. C. & Alder, B. J. 2008 Scaling of atomistic fuid dynamics simulations. Phys. Rev. E, 78, 045 301.
43. Kamm, J. R. 1999 LANL Report LA-UR-99-2783. Los Alamos, NM: Los Alamos National Laboratory.
44. Kevlahan, N. K.-R. 1997 The vorticity jump across a shock in a non-uniform flow. J. Rev. Fluid Mech. 341, 371-384. (doi:10.1017/ S0022112097005752) (Pubitemid 27405483)
45. Kontorovich, V. M. 1959 Reflection and refraction of sound by shock waves. Akusticheskii. Zh. 5, 320-330.
46. 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. (doi:10.1063/1.1321264) (Pubitemid 32015477)
47. Krasny, R. 1987 Computation of vortex sheet roll-up in the Trefftz plane. J. Fluid Mech. 184, 123-155. (doi:10.1017/S0022112087002830) (Pubitemid 18536609)
48. Landau, L. D. & Lifshitz, E. M. 1987 Fluid mechanics. New York, NY: Pergamon.
49. Lehmberg, R. H., Schmitt, A. J. & Bodner, S. E. 1987 Theory of induced spatial incoherence. J. Appl. Phys. 62, 2680-2701. (doi:10.1063/1. 339419)
50. Lombardini, M. & Pullin, D. I. 2009 Startup process in the Richtmyer-Meshkov instability. Phys. Fluids 21 044 104.
51. Manheimer, W. M. & Colombant, D. G. 1984 Slabmodel for Rayleigh-Taylor stabilization by vortex sheeding, compressibility, thermal conduction and ablation. Phys. Fluids 27, 983-993. (doi:10.1063/1.864689)
52. Matsui, N., Mima, K., Honda, M. & Nishiguchi, A. 1999 Analysis of rippled shock-wave propagation and ablation-front stability by theory and hydrodynamic simulation. J. Plasma Phys. 61, 43-50. (doi:10.1017/ S0022377898007260)
53. Matsuoka, C. & Nishihara, K. 2006a Vortex core dynamics and singularity formations in incompressible Richtmyer-Meshkov instability. Phys. Rev. E 73, 026304. [Erratum in Phys. Rev. E 2006 74, 049 902.]
54. Matsuoka, C. & Nishihara, K. 2006b Fully nonlinear evolution of a cylindrical vortex sheet in incompressible Richtmyer-Meshkov instability. Phys. Rev. E 73, 055304(R).
55. Matsuoka, C. & Nishihara, K. 2006c Analytical and numerical study on a vortex sheet in incompressible Richtmyer-Meshkov instability in cylindrical geometry. Phys. Rev. E 74, 066 303.
56. Matsuoka, C. & Nishihara, K. 2008 Multi-mode character of the nonlinear dynamics of a vortex sheet in Rayleigh-Taylor and Richtmyer-Meshkov instabilities. J. Phys. Conf. Ser. 112, 022 020.
57. Matsuoka, C., Nishihara, K. & Fukuda, Y. 2003 Nonlinear evolution of an interface in the Richymyer-Meshkov instability. Phys. Rev. E 67, 036 301. [Erratum in Phys. Rev. E 2003 68, 029 902.]
58. Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Sov. Fluid Dynamics 4, 101-105. (doi:10.1007/BF01015969)
59. Meyer, K. A. & Blewett, P. J. 1972 Numerical investigation of the stability of a shock-accelerated interface between two fluids. Phys. Fluids 15, 753-763. (doi:10.1063/1.1693980)
60. Mikaelian, K. 1994 Freeze-out and the effect of compressibility in the Richtmyer-Meshkov. Phys. Fluids 6, 356-368. (doi:10.1063/1.868091)
61. Mikhailov, A. L. 2007 Hydrodynamics instabilities in solid media-from the object of investigation to the investigation tool. Phys. Mesomech. 10, 265-274. (doi:10.1016/j.physme.2007.11.005)
62. Miller, G. H. & Ahrens, T. J. 1991 Shock wave viscosity measurement. Rev. Mod. Phys. 63, 919-948. (doi:10.1103/RevModPhys.63.919)
63. Mishin, M. J., Mehl, Y., Papaconstantopoulos, D. A., Voter, A. F. & Kress, J. D. 2003 Structural stability in lattice defects in copper: ab initio, tight-binding and embedded-atom calculations. Phys. Rev. B 63, 224 106.
64. Nishihara, K., Ishizaki, R., Wouchuk, J. G., Fukuda, Y. & Shimuta, Y. 1998 Hydrodynamic perturbation growth in start-up phase in laser implosion. Phys. Plasmas 5, 1945-1952. (doi:10.1063/1.872864) (Pubitemid 128598011)
65. Piriz, A. R., Sanz, J. & Ibañez, L. F. 1997 Rayleigh-Taylor instability of steady ablation fronts: the discontinuity model revisited. Phys. Plasmas 4, 1117-1126. (doi:10.1063/1.872200) (Pubitemid 127630377)
66. Piriz, A. R., Lopez Cela, J. J., Tahir, N. A. & Hoffmann, D. H. H. 2008 Richtmyer-Meshkov instability in elastic-plastic media. Phys. Rev. E 78, 056 401.
67. Poggi, F., Thorembey, M.-H. & Rodriguez, G. 1998 Velocity measurements in turbulent gaseous mixtures induced by Richtmyer-Meshkov instability. Phys. Fluids 10, 2698-2700. (doi:10.1063/1.869794) (Pubitemid 128599797)
68. Pullin, D. I. 1982 Numerical studies of surface-tension effects in nonlinear Kelvin-Helmholtz and Rayleigh-Taylor instability. J. Fluid Mech. 119, 507-537. (doi:10.1017/S0022112082001463)
69. Richtmyer, R. D. 1960 Taylor instability in a shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297-319. (doi:10.1002/cpa. 3160130207)
70. Rott, N. 1956 Diffraction of a weak shock with vortex generation. J. Fluid Mech. 1, 111-128. (doi:10.1017/S0022112056000081)
71. Saffman, P. G. 1992 Vortex dynamics. Cambridge, UK: Cambridge University Press.
72. Sakagami, H. & Nishihara, K. 1990a Rayleigh-Taylor instability on the pusher-fuel contact surface of stagnating targets. Phys. Fluids B 2, 2715-2730. (doi:10.1063/1.859395)
73. Sakagami, H. & Nishihara, K. 1990b Three-dimensional Rayleigh-Taylor instability of spherical system. Phys. Rev. Lett. 65, 432-435. (doi:10.1103/PhysRevLett.65.432)
74. Sanz, J. 1994 Self-consistent analytical model of the Rayleigh-Taylor instability in inertial confinement fusion. Phys. Rev. Lett. 73, 2700-2703. (doi:10.1103/PhysRevLett.73.2700) (Pubitemid 24976073)
75. Sanz, J. 1996 Self-consistent analytical model of the Rayleigh-Taylor instability in inertial confinement fusion. Phys. Rev. E 53, 4026-4045. (doi:10.1103/PhysRevE.53.4026)
76. Skupsky, S., Short, R. W., Kesseler, R. S., Craxton, R. S., Letzring, S. & Soures, J. M. 1989 Improved laser-beam uniformity using the angular dispersion of frequency-modulated light. J. Appl. Phys. 68, 3456-3462. (doi:10.1063/1.344101)
77. Sohn, S. I. 2004 Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Phys. Rev. E 69, 036 703.
78. Takabe, H., Nishihara, K. & Taniuti, T. 1978 Deflagration waves in laser compression. I. J. Phys. Soc. Japan 45, 2001-2008. (doi:10.1143/JPSJ.45. 2001)
79. Taylor, R. J., Velikovich, A. L., Dahlburg, J. P. & Gardner, J. H. 1997 Saturation of laser imprint on ablatively driven plastic targets. Phys. Rev. Lett. 79, 1861-1864. (doi:10.1103/ PhysRevLett.79.1861)
80. Vandenboomgaerde, M., Mugler, C. & Gauthier, S. 1998 Impulsive model for the Richtmyer- Meshkov instability. Phys. Rev. E 58, 1874-1882. (doi:10.1103/PhysRevE.58.1874)
81. Vandenboomgaerde, M., Gauthier, S. & Mügler, C. 2002 Nonlinear regime of a multimode Richtmyer-Meshkov instability: a simplified perturbation theory. Phys. Plasmas 14, 1111-1122. (Pubitemid 34305936)
82. Velikovich, A. L. 1996 Analytic theory of Richtmyer-Meshkov instability for the case of reflected rarefaction wave. Phys. Fluids 8, 1666-1679. (doi:10.1063/1.868938)
83. Velikovich, A. L. & Phillips, L. 1996 Instability of a plane centered rarefaction wave. Phys. Fluids 8, 1107-1118. (doi:10.1063/1.868889) (Pubitemid 126624765)
84. Velikovich, A. L., Dahlburg, J. P., Gardner, J. H. & Taylor, R. J. 1998 Saturation of perturbation growth in ablatively driven planar laser targets. Phys. Plasmas 5, 1491-1505. (doi:10.1063/ 1.872808)
85. Velikovich, A. L., Dahlburg, J. P., Schmitt, A. J., Gardner, J. H., Phillips, L. P., 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. (doi:10.1063/1.873986)
86. Velikovich, A. L., Wouchuk, J. G., Huete Ruiz de Lira, C., Metzler, N., Zalesak, S. & Schmitt, A. J. 2007 Shock front distortion and Richtmyer-Meshkov-type growth caused by a small preshock nonuniformity. Phys. Plasmas 14, 072 706. (Pubitemid 47192196)
87. Wheatley, V., Pullin, D. & Samtaney, R. 2005. Stability of an impulsively accelerated density interface in magnetohydrodynamics. Phys. Rev. Lett. 95, 125 002. (Pubitemid 40230949)
88. Wouchuk, J. G. 2001a Growth rate of the linear Richtmyer-Meshkov instability when a shock is reflected. Phys. Rev. E 63, 056 303.
89. Wouchuk, J. G. 2001b Growth rate of the Richtmyer-Meshkov instability when a rarefaction is reflected. Phys. Plasmas 8, 2890-2907. (doi:10.1063/1.1369119) (Pubitemid 33694335)
90. Wouchuk, J. G. & Carretero, R. 2003 Linear perturbation growth at the trailing edge of a rarefaction wave. Phys. Plasmas 10, 4237-4252. (doi:10.1063/1.1618773)
91. Wouchuk, J. G. & Cavada, J. L. 2004 Spontaneous acoustic emission of a corrugated shock wave in the presence of a reflecting surface. Phys. Rev. E 70, 046 303.
92. Wouchuk, J. G. & Nishihara, K. 1996 Linear perturbation growth at a shocked interface. Phys. Plasmas 3, 3761-3776. (doi:10.1063/1.871940) (Pubitemid 126589894)
93. Wouchuk, J. G. & Nishihara, K. 1997 Asymptotic growth in the linear Richtmyer-Meshkov instability. Phys. Plasmas 4, 1028-1038. (doi:10.1063/1. 872191) (Pubitemid 127630366)
94. Wouchuk, J. G. & Nishihara, K. 2004 Normal velocity freeze-out of the Richtmyer-Meshkov instability when a shock is reflected. Phys. Rev. E 70, 026 305.
95. Wouchuk, J. G. & Piriz, A. R. 1995 Growth rate reduction of the Rayleigh-Taylor instability by ablative convection. Phys. Plasmas 2, 493-500. (doi:10.1063/1.870974)
96. Wouchuk, J. G., Huete Ruiz de Lira, C. & Velikovich, A. L. 2009 Analytical linear theory for the interaction of a planar shock wave with an isotropic turbulent vorticity field. Phys. Rev. E 79, 066 315.
97. Yang, Y., Zhang, Q. & Sharp, D. H. 1994 Small amplitude theory of Richtmyer-Meshkov instability. Phys. Fluids 6, 1856-1873. (doi:10.1063/1.868245)
98. 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. (doi:10.1146/annurev.fluid.31.1.495) (Pubitemid 36175099)
99. 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. (doi:10.1017/ S0022112097008045)
100. 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, 419-421. (doi:10.1063/1. 1423932) (Pubitemid 34057296)
101. Zaidel, P. M. 1960 Shock wave from a slightly curved piston. J. Appl. Math. Mech. 24, 316-327.
102. Zhakhovskii, V. V., Nishihara, K. & Abe, M. 2002 Molecular dynamics simulation on stability of converging shocks. In Proc. 2nd Int. Conf. on Inertial Fusion Sciences and Applications (IFSA 2001 ), Kyoto, Japan, 9-14 September 2001, pp. 106-109. Paris, France: Elsevier.
103. Zhakhovskii, V. V., Zybin, S. V., Abarzhi, S. I. & Nishihara, K. 2006 Atomistic dynamics of the Richtmyer-Meshkov instability in cylindrical and planar geometries. In Proc. Conf. American Physical Society Topical Group on Shock Compression of Condensed Matter, Baltimore, Maryland, 31 July-5 August 2005, vol.845, pp. 433-436. New York, NY: Springer.
104. Zhang, Q. & Sohn, S. I. 1997 Nonlinear theory of unstable fluid mixing driven by shock wave. Phys. Fluids 9, 1106-1124. (doi:10.1063/1.869202) (Pubitemid 127651254)
105. Zybin, S. V., Zhakhovskii, V. V., Bringa, E. M. & Abarzhi, S. I. 2006 Molecular dynamics simulations of the Richtmyer-Meshkov instability in shock loaded solids. In Proc. Conf. American Physical Society Topical Group on Shock Compression of Condensed Matter, Baltimore, Maryland, 31 July-5 August 2005, vol.845, pp. 437-441. New York, NY: Springer.