A comparative study of the turbulent Rayleigh-Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration

Physics of Fluids

Volumn 16, Issue 5, 2004, Pages 1668-1693

  Dimonte, Guy ^a   Youngs, D L ^b   Dimits, A ^c   Weber, S ^c   Marinak, M ^c   Wunsch, S ^d   Garasi, C ^e   Robinson, A ^e   Andrews, M J ^f   Ramaprabhu, P ^f   Calder, A C ^g   Fryxell, B ^g   Biello, J ^g   Dursi, L ^g   MacNeice, P ^h   Olson, K ^h   Ricker, P ^g   Rosner, R ^g   Timmes, F ^g   Tufo, H ^g   Young, Y N ^g   Zingale, M ^g   more..

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b AWE   (United Kingdom)

^c LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^d SANDIA NATIONAL LABORATORIES   (United States)

^e SANDIA NATIONAL LABORATORIES   (United States)

^f TEXAS A AND M UNIVERSITY   (United States)

^g UNIVERSITY OF CHICAGO   (United States)

^h NASA GODDARD SPACE FLIGHT CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUBBLES (IN FLUIDS); COMPUTER SIMULATION; PERTURBATION TECHNIQUES; SENSITIVITY ANALYSIS; TURBULENCE;

DENSITY DILUTION; INTERFACE RECONSTRUCTION (IR); NONLINEAR COUPLING; WAVELENGTH MODES;

FLUID DYNAMICS;

BUBBLE; MATHEMATICAL ANALYSIS; MIXING; RAYLEIGH NUMBER; TAYLOR DISPERSION;

EID: 2442644995     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1688328     Document Type: Article

References (81)

1. Lord Rayleigh, Scientific Papers II (Cambridge University Press. Cambridge, 1900), p. 200.
2. G. I. Taylor, "The instability of liquid surfaces when accelerated in a direction perpendicular to their plane,2: Proc. R. Soc. London, Ser. A 201. 192 (1950).
3. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961).
4. H. W. Emmons, C. T. Chang, and B. C. Watson, "Taylor instability of finite surface waves," J. Fluid Mech. 7, 177 (1960).
5. D. T. Dumitrescu, "Stromung an einer Luftblase im senkhrecten Rohr." Z. Angew. Math. Mech. 23, 139 (1943).
6. 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).
7. 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).
8. R. S. Scorer, "Experiments on convection of isolated masses of buoyant fluid," J. Fluid Mech. 2, 583 (1957).
9. 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).
10. D. Layzer, "On the instability of superposed fluids in a gravitational field," Astrophys. J. 122, 1 (1955).
11. H. J. Kull, "Theory of the Rayleigh-Taylor instability," Phys. Rep. 206, 197 (1991).
12. J. Hecht, U. Alon, and D. Shvarts, "Potential flow models of Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts," Phys. Fluids 6. 4019 (1994).
13. G. Tryggvason and S. O. Unverdi, "Computations of three-dimensional Rayleigh-Taylor instability," Phys. Fluids A 2, 656 (1990).
14. 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).
15. X. L. Li, "A numerical study of three-dimensional bubble merger in the Rayleigh-Taylor instability," Phys. Fluids 8, 336 (1996).
16. X. L. Li, B. X. Jin, and J. Glimm, "Numerical study of 3D Rayleigh-Taylor instability through the TVD/AC scheme and parallel computation." J. Comput. Phys. 126, 343 (1996).
17. 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).
18. X. He, R. Zhang, S. Chen, and G. Doolen, "On the three-dimensional Rayleigh-Taylor instability," Phys. Fluids 11, 1143 (1999).
19. K. Kadau, T. Germann, N. Hadjiconstantinou, P. Lambdahl, G. Dimonte, B. L. Holian, and B. Alder, "Nanohydrodynamics simulations: An atomistic view of the Rayleigh-Taylor instability," Proc. Natl. Acrid. Sci. U.S.A. (to be published).
20. G. Birkhroff, "Taylor instability and laminar mixing," University of California Report No. LA-1862, 1955.
21. N. A. Inugamov, "Turbulent stage of the Rayleigh-Taylor instability," Sov. Tech. Phys. Lett. 4, 299 (1978).
22. N. A. Inogamov, A. V. Chekhlov, Al. Yu. Dem'yanov, S. I. Anisimov, and O. M. Belotserkovskii, in Proceedings of the Third International Workshop on Physics Compressible Turbulent Mixing, edited by R. Dautray (Commissariat Energie Atomique, Cesta, France, 1991), p. 409.
23. N. N. Anuchina, Yu. A. Kucherenko, V. E. Neuvazhaev, V. N. Ogibina, L. I. Shibarshov, and V. G. Yakovlev, "Turbulent mixing at an accelerating interface between liquids of different densities," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 6, 157 (1978).
24. K. I. Read, "Experimental investigation of turbulent mixing by Rayleigh-Taylor instability," Physica D 12, 45 (1984).
25. D. L. Youngs, "Modeling turbulent mixing by Rayleigh-Taylor instability," Physica D 37, 270 (1989).
26. 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).
27. 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," in Proceedings of the Third International Workshop on Physics Compressible Turbulent Mixing, edited by R. Dautray (Commissariat Energie Atomique, Cesta, France, 1991), p. 427.
28. G. Dimonte and M. Schneider, "Turbulent Rayleigh-Taylor instability experiments with variable acceleration," Phys. Rev. E 54, 3740 (1996).
29. M. Schneider, G. Dimonte, and B. Remington, "Large and small scale structure in Rayleigh-Taylor mixing," Phys. Rev. Lett. 80, 3507 (1998).
30. G. Dimonte and M. Schneider, "Density ratio dependence of Rayleigh-Taylor mixing for sustained and impulsive acceleration histories," Phys. Fluids 12, 304 (2000).
31. D. L. Youngs, "Numerical simulation of turbulent mixing by Rayleigh-Taylor instability," Physica D 12, 32 (1984).
32. 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).
33. 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).
34. C. Cherfills and K. O. Mikaelian, "Simple model for the turbulent mixing width at an ablating surface," Phys. Fluids 8, 522 (1996).
35. N. N. Anuchina, V. A. Gordeichuk, N. S. Eskov, O. S. Ilyutina, O. M. Kozyrev, and V. I. Volkov, in Proceedings of the 6th International on Workshop Physics Compressible Turbulent Mixing, edited by G. Jourdan and L. Houas (Imprimerie Caractere, Marseille, France, 1997), p. 24.
36. X. He, S. Chen, and R. Zhang, "A lattice Boltzmann scheme fir incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability," J. Comput. Phys. 152, 642 (1999).
37. T. Clark, "A numerical study of the statistics of a 2D Rayleigh-Taylor mixing layer," Phys. Fluids 15, 2413 (2003).
38. D. L. Youngs, "Three-dimensional numerical simulation of turbulent mixing by Rayleigh-Taylor instability," Phys. Fluids A 3, 1312 (1991).
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. A. W. Cook and P. E. Dimotakis, "Transition stages of Rayleigh-Taylor instability between miscible fluids," J. Fluid Mech. 443, 69 (2001).
42. Y.-N. Young, H. Tufo, A. Dubey, and R. Rosner. "On the miscible Rayleigh-Taylor instability: Two and three dimensions," J. Fluid Mech. 447, 377 (2001).
43. J. Glimm, J. W. Grove, X. L. Li, W. Oh, and D. H. Sharp, "A critical analysis of Rayleigh-Taylor growth rates," J. Comput. Phys. 169, 652 (2001);
44. E. George, J. Glimm, X.-L. Li, A. Marchese, and Z.-L. Xu, "A comparison of experimental theoretical, and numerical simulation Rayleigh-Taylor mixing rates," Proc. Nat. Acad. Sci., U.S.A. 99, 2587 (2002).
45. D. Oron. L. Arazi, D. Kartoon, A. Rikanati, U. Alon, and D. Shvarts, "Dimensionality dependence of Rayleigh-Taylor and Richtmyer-Meshkov instability late-time scaling laws," Phys. Plasmas 8, 2883 (2001).
46. J. A. Zufiria, "Bubble competition in Rayleigh-Taylor instability," Phys. Fluids 31, 440 (1988).
47. J. Glimm and X. L. Li, "Validation of Sharp-Wheeler merger model from experimental and computational data," Phys. Fluids 31, 2077 (1988).
48. D. Shvarts, U. Alon, D. Ofer, R. L. McCrory, and C. P. Verdon, "Nonlinear evolution of multimode Rayleigh-Taylor instability in two and three dimensions," Phys. Plasmas 2, 2465 (1995).
49. 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).
50. G. Dimonte, "Dependence of turbulent Rayleigh-Taylor (RT) instability on initial conditions," Phys. Rev. E (to be published).
51. S. W. Haan, "Onset of nonlinear saturation for Rayleigh-Taylor growth in the presence of a full spectrum of modes," Phys. Rev. A 39, 5812 (1989).
52. S. W. Haan, "Weakly nonlinear hydrodynamic instabilities in inertial fusion," Phys. Fluids B 3, 2349 (1991).
53. 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).
54. J. Glimm, D. Saltz, and D. H. Sharp, "Statistical evolution of chaotic fluid mixing," Phys. Rev. Lett. 80, 712 (1998).
55. J. D. Ramshaw, "Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration," Phys. Rev. E 58, 5834 (1998).
56. G. Dimonte, "Spanwise homogeneous buoyancy-drag model for Rayleigh-Taylor mixing and experimental verification." Phys. Plasmas 7, 2255 (2000).
57. V. A. Andronov, S. M. Bakhrakh, V. N. Mokhov, V. V. Nikiforov, and A. V. Pevnitskii, "Effect of turbulent mixing on the compression of laser targets," JETP Lett. 29, 56 (1979).
58. S. Gauthier and M. Bonnet, "A k-ε model for turbulent mixing in shocktube flows induced by Rayleigh-Taylor instability," Phys. Fluids A 2, 1685 (1990).
59. R. D. Blevins, Applied Fluid Dynamics Handbook (Van Nostrand Reinhold, New York, 1984), p. 332.
60. E. S. Oran and J. P. Boris, Numerical Simulation of Reactive Flow, 2nd ed. (Cambridge University Press, Cambridge, 2001).
61. D. L. Youngs, Numerical Methods for Fluid Dynamics, edited by K. W. Morton and M. J. Baines (Academic, London, 1982).
62. B. van Leer, "Towards the ultimate conservative difference scheme IV. A new approach to numerical convection," J. Comput. Phys. 23, 276 (1977).
63. R. B. DeBar, "A method in 2D Eulerian hydrodynamics," Lawrence Livermore National Laboratory Report No. UCID- 19683 (1974).
64. P. Colella and P. Woodward, "The piecewise parabolic method (PPM) for gas-dynamic simulations," J. Comput. Phys. 54, 174 (1984).
65. P. MacNeice, K. M. Olson, C. Mobarry, R. de Fainchtein, and C. Packer, "PARAMESH: A parallel adaptive mesh refinement community toolkit," Comput. Phys. Commun. 126, 330 (2000).
66. W. Gropp, E. Lusk, and A. Skjellum, Using MPJ: Portable Parallel Programming with the Message Passing Interface, 2nd ed. (MIT Press, Cambridge, MA, 1999).
67. B. Fryxell, K. Olson, P. Ricker, F. X. Timmes, M. Zingale, D. Q. Lamb. P. MacNiece, R. Rosner, J. W. Truran, and H. Tufo, "FLASH: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes," Astrophys. J., Suppl. Ser. 131, 273 (2000).
68. A. C. Calder, L. J. Dursi, B. Fryxell, T. Plewa, V. G. Weirs, T. Dupont, H. F. Robey, J. O. Kane, R. P. Drake, B. A. Remington, G. Dimonte, J. Hayes, J. M. Stone, P. M. Ricker, F. X. Timmes, M. Zingale, and K. Olson, "On validating an astrophysical simulation code," Astrophys. J., Suppl. Ser. 143, 201 (2002).
69. D. H. Porter and P. R. Woodward, "High-resolution simulations of compressible convestion using the piecewise-parabolic method," Astrophys. J., Suppl. Ser. 93, 309 (1994).
70. S. K. Godunov, "A difference method for the numerical solution of discontinuities in hydrodynamic equations," Mathematic Sb. 47, 271 (1959) (in Russian).
71. B. van Leer, "Towards the ultimate conservative difference scheme V. A second order sequel to Gudunov's method," J. Comput. Phys. 32, 101 (1979).
72. M. J. Andrews, "Accurate computation of convective transport in two-phase flow," Int. J. Numer. Methods Fluids 21, 205 (1995).
73. M M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, "Three-dimensional HYDRA simulations of NIF targets," Phys. Plasmas 8, 2275 (2001).
74. J. S. Peery and D. E. Carroll, "Multimaterial ALE methods in unstructured grids," Comput. Methods Appl. Mech. Eng. 187, 591 (2000).
75. D. L. Youngs, "An interface tracking method for a 3D Eulerian hydrodynamics code," AWE, AWRE/44/92/35, April 1987.
76. A. C. Robinson and J. W. Swegle, "Acceleration instability in elasticplastic solids. II analytical techniques," J. Appl. Phys. 66, 2859 (1989).
77. B. J. Daly, "Numerical study of two fluid Rayleigh-Taylor instability," Phys. Fluids 10, 297 (1967).
78. M. Wilson and M. J. Andrews, "Spectral measurements of Rayleigh-Taylor mixing at small Atwood number," Phys. Fluids 14, 938 (2002).
79. A. W. Cook and Y. Zhou, "Energy transfer in Rayleigh-Taylor instability," Phys. Rev. E 66, 026312 (2002).
80. D. L. Youngs, "Application of MILES to Rayleigh-Taylor and Richtmyer-Meshkov mixing," AIAA Paper No. 2003-4102 (2003).
81. S. B. Dalziel, P. F. Linden, and D. L. Youngs, "Self-similarity and internal structure of turbulence induced by Rayleigh-Taylor instability," J. Fluid Mech. 399, 1 (1999).