Density ratio dependence of Rayleigh-Taylor mixing for sustained and impulsive acceleration histories

Physics of Fluids

Volumn 12, Issue 2, 2000, Pages 304-321

  Dimonte, Guy ^a   Schneider, Marilyn ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; DENSITY; HYDRODYNAMICS; MIXING;

EID: 0034079449     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.870309     Document Type: Article

References (75)

1. Lord Rayleigh, Scientific Papers (Cambridge University Press, Cambridge, 1900), Vol. II, p. 200.
2. G. I. Taylor, "The instability of liquid surfaces when accelerated in a direction perpendicular to their plane," Proc. R. Soc. London, Ser. A 201, 192 (1950).
3. R. D. Richtmyer, "Taylor instability in shock acceleration of compressible fluids," Commun. Pure Appl. Math. 13, 297 (1960).
4. E. E. Meshkov, "Instability of the interface of two gases by a shock wave," Izv. Acad. Sci. USSR Fluid Dynamics 4, 101 (1969).
5. J. D. Lindl, Inertial Confinement Fusion (Springer, New York, 1998).
6. V. A. Andronov, S. M. Bakhrakh, V. N. Mokohov, V. V. Nikiforov, and A. V. Pevnitskii, "Effect of turbulent mixing on the compression of laser targets," JETP Lett. 29, 56 (1979).
7. G. Dimonte, "Nonlinear evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities," Phys. Plasmas 6, 2009 (1999).
8. D. J. Lewis, "The instability of liquid surfaces when accelerated in direction perpendicular to their planes," Proc. R. Soc. London, Ser. A 202, 81 (1950).
9. H. W. Emmons, C. T. Chang, and B. C. Watson, "Taylor instability of finite surface waves," J. Fluid Mech. 7, 177 (1960).
10. R. M. Davies and G. I. Taylor, "The mechanics of large bubbles rising through extended liquids and through liquids in tubes," Proc. R. Soc. London, Ser. A 200, 375 (1950).
11. R. Collins, "The effect of a containing cylindrical boundary on the velocity of a large gas bubble in a liquid," J. Fluid Mech. 28, 97 (1967).
12. D. Layzer, "On the instability of superposed fluids in a gravitational field," Astrophys. J. 122, 1 (1955).
13. R. Menikoff and C. Zemach, "Rayleigh-Taylor instability and the use of conformal maps for ideal fluid flow," J. Comput. Phys. 51, 28 (1983).
14. H. J. Kull, "Nonlinear free-surface Rayleigh-Taylor instability," Phys. Rev. A 33, 1957 (1986).
15. J. Hecht, U. Alon, and D. Shvarts, "Potential flow models of Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts," Phys. Fluids 6, 4019 (1994).
16. U. Alon, J. Hecht, D. Ofer, and D. Shvarts, "Power laws and similarity of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts at all density ratios," Phys. Rev. Lett. 74, 534 (1995).
17. Q. Zhang, "Analytical solutions of Layzer-type approach to unstable interfacial fluid mixing," Phys. Rev. Lett. 81, 3391 (1998).
18. G. R. Baker, D. I. Meiron, and S. A. Orszag, "Vortex simulations of the Rayleigh-Taylor instability," Phys. Fluids 23, 1485 (1980).
19. D. L. Youngs, "Numerical simulation of turbulent mixing by Rayleigh-Taylor instability," Physica D 12, 32 (1984).
20. G. Tryggvason and S. O. Unverdi, "Computations of three-dimensional Rayleigh-Taylor instability," Phys. Fluids A 2, 656 (1990).
21. J. Hecht, D. Offer, U. Alon, D. Shvarts, S. A. Orszag, and R. L. McCrory, "Three-dimensional simulations and analysis of the nonlinear stage of the Rayleigh-Taylor instability," Laser Part. Beams 13, 423 (1995).
22. X. L. Li, "A numerical study of three-dimensional bubble merger in the Rayleigh-Taylor instability," Phys. Fluids 8, 336 (1996).
23. K. A. Meyer and P. J. Blewett, "Numerical investigation of the stability of a shock-accelerated interface between two fluids," Phys. Fluids 15, 753 (1972).
24. T. Pham and D. I. Meiron, "A numerical study of Richtmyer-Meshkov instability in continuously stratified fluids," Phys. Fluids A 5, 344 (1993).
25. G. Fraley, "Rayleigh-Taylor stability for a normal shock wave-density discontinuity interaction," Phys. Fluids 29, 376 (1986).
26. A. L. Velikovich, "Analytic theory of Richtmyer-Meshkov instability for the case of reflected rarefaction wave," Phys. Fluids 8, 1666 (1996).
27. R. F. Benjamin and J. N. Fritz, "Shock loading a rippled interface between liquids of different densities," Phys. Fluids 30, 331 (1987).
28. A. N. Aleshin, E. V. Lazareva, S. G. Zaitsev, V. B. Rozanov, E. G. Gamalii, and I. G. Lebo, "Linear, nonlinear and transient stages in development of Richtmyer-Meshkov instability," Sov. Phys. Dokl. 35, 159 (1990).
29. G. Dimonte and B. Remington, "Richtmyer-Meshkov experiments on Nova laser at high compression," Phys. Rev. Lett. 70, 1806 (1993); G. Dimonte, C. E. Frerking, M. Schneider, and B. Remington, "Richtmyer-Meshkov instability with strong radiatively driven shocks," Phys. Plasmas 3, 614 (1996).
30. G. Dimonte and B. Remington, "Richtmyer-Meshkov experiments on Nova laser at high compression," Phys. Rev. Lett. 70, 1806 (1993); G. Dimonte, C. E. Frerking, M. Schneider, and B. Remington, "Richtmyer-Meshkov instability with strong radiatively driven shocks," Phys. Plasmas 3, 614 (1996).
31. A. L. Velikovich and G. Dimonte, "Nonlinear perturbation theory of incompressible Richtmyer-Meshkov instability," Phys. Rev. Lett. 76, 3112 (1996).
32. R. L. Holmes, G. Dimonte, B. Fryxell, M. L. Gittings, J. W. Grove, M. Schneider, D. H. Sharp, A. L. Velikovich, R. P. Weaver, and Q. Zhang, "Richtmyer-Meshkov instability growth: Experiment, simulation and theory," J. Fluid Mech. 389, 55 (1999).
33. D. L. Youngs, "Three-dimensional numerical simulation of turbulent mixing by Rayleigh-Taylor instability," Phys. Fluids A 3, 1312 (1991).
34. N. J. Zabusky, "Vortex paradigm for accelerated inhomogeneous flows: Visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov environments," Annu. Rev. Fluid Mech. 31, 495 (1999).
35. D. L. Youngs, "Modeling turbulent mixing by Rayleigh-Taylor instability," Physica D 37, 270 (1989).
36. J. Glimm, X. L. Li, R. Menikoff, D. H. Sharp, and Q. Zhang, "A numerical study of bubble interactions in Rayleigh-Taylor instability for compressible fluids," Phys. Fluids A 2, 2046 (1990).
37. N. Freed, D. Ofer, D. Shvarts, and S. O. Orszag, "Two-phase flow analysis of self-similar turbulent mixing by Rayleigh-Taylor instability," Phys. Fluids A 3, 912 (1991).
38. X. L. Li, "Study of three-dimensional Rayleigh-Taylor instability in compressible fluids through level set method and parallel computation," Phys. Fluids A 5, 1904 (1993).
39. D. L. Youngs, "Numerical simulation of mixing by Rayleigh-Taylor and Richtmyer-Meshkov instabilities," Laser Part. Beams 12, 725 (1994).
40. P. F. Linden, J. M. Redondo, and D. L. Youngs, "Molecular mixing in Rayleigh-Taylor instability," J. Fluid Mech. 265, 97 (1994).
41. C. Cherfills and K. O. Mikaelian, "Simple model for the turbulent mixing width at an ablating surface," Phys. Fluids 8, 522 (1996).
42. D. H. Sharp, "An overview of Rayleigh-Taylor instability," Physica D 12, 3 (1984).
43. J. A. Zufiria, "Bubble competition in Rayleigh-Taylor instability," Phys. Fluids 31, 440 (1988).
44. J. Glimm and X. L. Li, "Validation of Sharp-Wheeler merger model from experimental and computational data," Phys. Fluids 31, 2077 (1988).
45. S. W. Haan, "Weakly nonlinear hydrodynamic instabilities in inertial fusion," Phys. Fluids B 3, 2349 (1991).
46. S. Gauthier and M. Bonnet, "A k-∈ model for turbulent mixing in shock-tube flows induced by Rayleigh-Taylor instability," Phys. Fluids A 2, 1685 (1990).
47. J. C. Hanson, P. A. Rosen, T. J. Goldsack, K. Oades, P. Fieldhouse, N. Cowperthwaite, D. L. Youngs, N. Mawhinney, and A. J. Baxter, "Radiation driven planar foil instability and mix experiments at the AWE HELEN laser," Laser Part. Beams 8, 51 (1990).
48. Y. Chen, J. Glimm, D. H. Sharp, and Q. Zhang, "A two-phase flow model of the Rayleigh-Taylor mixing zone," Phys. Fluids 8, 816 (1996).
49. J. Glimm, D. Saltz, and D. H. Sharp, "Statistical evolution of chaotic fluid mixing," Phys. Rev. Lett. 80, 712 (1998).
50. J. D. Ramshaw, "Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration," Phys. Rev. E 58, 5834 (1998).
51. G. Dimonte, "Spanwise homogeneous buoyancy-drag model for Rayleigh-Taylor mixing and experimental verification," accepted for publication in Phys. Plasmas (1999).
52. K. I. Read, "Experimental investigation of turbulent mixing by Rayleigh-Taylor instability," Physica D 12, 45 (1984).
53. M. J. Andrews and D. B. Spalding, "A simple experiment to investigate two-dimensional mixing by Rayleigh-Taylor instability," Phys. Fluids A 2, 922 (1990).
54. P. F. Linden and J. M. Redondo, "Molecular mixing in Rayleigh-Taylor instability. I. Global mixing," Phys. Fluids A 3, 1269 (1991).
55. Yu. A. Kucherenko, L. I. Shibarshov, V. I. Chitaikin, S. I. Balabin, and A. P. Pylaev, "Experimental study of the gravitational turbulent mixing self-similar mode," Proceedings of the Third International Workshop on Physics Compressible Turbulent Mixing, edited by R. Dautray (Commissariat Energie Atomique, Cesta, France, 1991), p. 427.
56. G. Dimonte and M. Schneider, "Turbulent Rayleigh-Taylor instability experiments with variable acceleration," Phys. Rev. E 54, 3740 (1996).
57. M. Schneider, G. Dimonte, and B. Remington, "Large and small scale structure in Rayleigh-Taylor mixing," Phys. Rev. Lett. 80, 3507 (1998).
58. G. I. Barenblatt, "Self-similar turbulence propagation from an instantaneous plane source," in Nonlinear Dynamics and Turbulence, edited by G. I. Barenblatt, G. loos, and D. D. Joseph (Pitman, Boston, 1983), p. 48.
59. Yu. A. Kucherenko, S. I. Balabin, R. Cherret, and J. F. Haas, "Experimental investigation into inertial properties of Rayleigh-Taylor turbulence," Laser Part. Beams 15, 25 (1997).
60. G. Dimonte, C. E. Frerking, and M. Schneider, "Richtmyer-Meshkov instability in the turbulent regime," Phys. Rev. Lett. 74, 4855 (1995); G. Dimonte and M. Schneider, "Turbulent Richtmyer-Meshkov instability experiments with strong radiatively driven shocks," Phys. Plasmas 4, 4347 (1997).
61. G. Dimonte, C. E. Frerking, and M. Schneider, "Richtmyer-Meshkov instability in the turbulent regime," Phys. Rev. Lett. 74, 4855 (1995); G. Dimonte and M. Schneider, "Turbulent Richtmyer-Meshkov instability experiments with strong radiatively driven shocks," Phys. Plasmas 4, 4347 (1997).
62. D. R. Farley, T. A. Peyser, P. L. Miller, L. M. Logory, P. E. Stry, and E. W. Burke, "Experimental investigation of compressible Richtmyer-Meshkov instability from a broad-spectrum multimode initial perturbation," Proceedings of the Sixth International Workshop on Physics Compressible Turbulent Mixing, edited by G. Jourdan and L. Houas (Marseille, France, 1997), p. 161.
63. V. A. Andronov, S. M. Bakhrakh, E. E. Meshkov, V. N. Mokhov, V. V. Nikiforov, A. V. Pevnitskii, and A. I. Tolshmyakov, "Turbulent mixing at contact surface accelerated by shock waves," Sov. Phys. JETP 44, 424 (1976).
64. S. G. Zaitsev, E. V. Lazareva, V. V. Chemukha, and V. M. Belyaev, "Intensification of mixing at interface between media of different densities upon the passage of a shock wave throught it," Sov. Phys. Dokl. 30, 579 (1985).
65. M. Brouillette and B. Sturtevant, "Experiments on the Richtmyer-Meshkov instability: Small=scale perturbations on a plane interface," Phys. Fluids A 5, 916 (1993); M. Vetter and B. Sturtevant, "Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface," Shock Waves 4, 247 (1995).
66. M. Brouillette and B. Sturtevant, "Experiments on the Richtmyer-Meshkov instability: Small=scale perturbations on a plane interface," Phys. Fluids A 5, 916 (1993); M. Vetter and B. Sturtevant, "Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface," Shock Waves 4, 247 (1995).
67. L. Houas and I. Chemouni, "Experimental investigation of Richtmyer-Meshkov instability in shock tube," Phys. Fluids 8, 614 (1996).
68. G. Dimonte, J. Morrison, S. Hulsey, D. Nelson, S. Weaver, A. Susoeff, R. Hawke, M. Schneider, J. Batteaux, D. Lee, and J. Ticehurst, "A linear electric motor to study turbulent hydrodynamics," Rev. Sci. Instrum. 67, 302 (1996).
69. Yu. A. Kucherenko, A. P. Pylaev, V. D. Murzakov, V. N. Popov, O. R. Komarov, V. E. Savel'ev, R. Cherret, and J. F. Haas, "Experimental study into the asymptotic stage of the separation of the turbulized mixtures in gravitationally stable mode," Laser Part. Beams 15, 17 (1997).
70. J. Lachaise, A. Garcia, A. Martinez, and R. Rousset, "Measurement of low interfacial tensions from diffuse reflection," Thin Solid Films 82, 55 (1981).
71. K. O. Mikaelian, "Turbulent energy at accelerating and shocked interfaces," Phys. Fluids A 2, 592 (1990).
72. C. P. DeNeef, J. H. Malmberg, and T. M. O'Neil, "Launched waves on a beam-plasma system," Phys. Rev. Lett. 30, 1032 (1973); G. Dimonte, "Experimental test of modulational theory and stochasticity of non-linear oscillations," Phys. Fluids 25, 604 (1982).
73. C. P. DeNeef, J. H. Malmberg, and T. M. O'Neil, "Launched waves on a beam-plasma system," Phys. Rev. Lett. 30, 1032 (1973); G. Dimonte, "Experimental test of modulational theory and stochasticity of non-linear oscillations," Phys. Fluids 25, 604 (1982).
74. R. Betti, R. L. McCrory, and C. P. Verdon, "Stability analysis of unsteady ablation fronts," Phys. Rev. Lett. 71, 3131 (1993).
75. Jeff Colvin (private communication, 1998).