Nonlinear evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Dimonte, G

doi:10.1063/1.873491

Nonlinear evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Conference · Sat Oct 31 23:00:00 EST 1998

DOI:https://doi.org/10.1063/1.873491· OSTI ID:5773

Dimonte, G ^[1]

LLNL

Scaled experiments on the nonlinear evolution of the Rayleigh- Taylor (RT) and Richtmyer-Meshkov (RM) instabilities are described under a variety, of conditions that occur in nature. At high Reynolds number, the mixing layer grows self-similarly - {alpha}{sub i}Agt{sup 2} for a constant acceleration (g), and as a power law t{sup {theta}{sub i}} for impulsive accelerations U{delta}(t) at low and high Mach numbers. The growth coefficients {alpha}{sub i} and {theta}{sub i} exponents are measured over a comprehensive range of Atwood numbers A. The RT instability is also investigated with Non- Newtonian materials which are independently characterized. A critical wavelength and amplitude for instability is observed associated with the shear modulus and tensile yield of the material. The results are applicable from supernova explosions to geophysical flows subject to these hydrodynamic instabilities.

View Conference

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA

Sponsoring Organization:: USDOE Office of Defense Programs (DP)

DOE Contract Number:: W-7405-ENG-48

OSTI ID:: 5773

Report Number(s):: UCRL-JC-132439; DP0210000; ON: DE00005773

Country of Publication:: United States

Language:: English

References (62)

A two‐phase flow model of the Rayleigh–Taylor mixing zone Chen, Yupin; Glimm, James; Sharp, David H. Physics of Fluids, Vol. 8, Issue 3 https://doi.org/10.1063/1.868863	journal	March 1996
The Aleutian Arc: Tectonic blocks, episodic subduction, strain diffusion, and magma generation Spence, William Journal of Geophysical Research, Vol. 82, Issue 2 https://doi.org/10.1029/JB082i002p00213	journal	January 1977
A numerical study of three‐dimensional bubble merger in the Rayleigh–Taylor instability Li, X. L. Physics of Fluids, Vol. 8, Issue 2 https://doi.org/10.1063/1.868789	journal	February 1996
Families of salt Domes in the gulf Coastal Province Selig, Franz; Wermund, E. G. GEOPHYSICS, Vol. 31, Issue 4 https://doi.org/10.1190/1.1439806	journal	August 1966
Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface Vetter, M.; Sturtevant, B. Shock Waves, Vol. 4, Issue 5 https://doi.org/10.1007/BF01416035	journal	March 1995
Island Arc Development: Some Observations, Experiments, and Speculations Marsh, B. D. The Journal of Geology, Vol. 87, Issue 6 https://doi.org/10.1086/628460	journal	November 1979
Statistical Evolution of Chaotic Fluid Mixing Glimm, James; Saltz, David; Sharp, David H. Physical Review Letters, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevLett.80.712	journal	January 1998
Two‐phase flow analysis of self‐similar turbulent mixing by Rayleigh–Taylor instability Freed, Nathan; Ofer, Dror; Shvarts, Dov Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5 https://doi.org/10.1063/1.857967	journal	May 1991
Dynamics of exploding plasmas in a magnetic field Dimonte, Guy; Wiley, L. G. Physical Review Letters, Vol. 67, Issue 13 https://doi.org/10.1103/PhysRevLett.67.1755	journal	September 1991
Electromagnetic Implosion of Spherical Liner Degnan, J. H.; Lehr, F. M.; Beason, J. D. Physical Review Letters, Vol. 74, Issue 1 https://doi.org/10.1103/PhysRevLett.74.98	journal	January 1995
Nonlinear Perturbation Theory of the Incompressible Richtmyer-Meshkov Instability Velikovich, Alexander L.; Dimonte, Guy Physical Review Letters, Vol. 76, Issue 17 https://doi.org/10.1103/PhysRevLett.76.3112	journal	April 1996
Richtmyer–Meshkov instability with strong radiatively driven shocks Dimonte, Guy; Frerking, C. Eric; Schneider, Marilyn Physics of Plasmas, Vol. 3, Issue 2 https://doi.org/10.1063/1.871889	journal	February 1996
Small amplitude theory of Richtmyer–Meshkov instability Yang, Yumin; Zhang, Qiang; Sharp, David H. Physics of Fluids, Vol. 6, Issue 5 https://doi.org/10.1063/1.868245	journal	May 1994
Behaviour of Laser-Produced Plasma in a Uniform Magnetic Field–Plasma Instabilities Okada, Shigefumi; Sato, Kohnosuke; Sekiguchi, Tadashi Japanese Journal of Applied Physics, Vol. 20, Issue 1 https://doi.org/10.1143/JJAP.20.157	journal	January 1981
Large-Larmor-radius interchange instability Ripin, B. H.; McLean, E. A.; Manka, C. K. Physical Review Letters, Vol. 59, Issue 20 https://doi.org/10.1103/PhysRevLett.59.2299	journal	November 1987
Large and Small Scale Structure in Rayleigh-Taylor Mixing Schneider, Marilyn B.; Dimonte, Guy; Remington, Bruce Physical Review Letters, Vol. 80, Issue 16 https://doi.org/10.1103/PhysRevLett.80.3507	journal	April 1998
A k ‐ε model for turbulent mixing in shock‐tube flows induced by Rayleigh–Taylor instability Gauthier, Serge; Bonnet, Michel Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 9 https://doi.org/10.1063/1.857576	journal	September 1990
Stability of sub‐Alfvénic plasma expansions Huba, J. D.; Hassam, A. B.; Winske, D. Physics of Fluids B: Plasma Physics, Vol. 2, Issue 7 https://doi.org/10.1063/1.859441	journal	July 1990
Interchange stability of an axisymmetric, average minimum-B magnetic mirror Ferron, John R. Physics of Fluids, Vol. 26, Issue 8 https://doi.org/10.1063/1.864377	journal	January 1983
Nonlinear Rayleigh-Taylor Evolution of a Three-Dimensional Multimode Perturbation Marinak, M. M.; Glendinning, S. G.; Wallace, R. J. Physical Review Letters, Vol. 80, Issue 20 https://doi.org/10.1103/PhysRevLett.80.4426	journal	May 1998
Acceleration instability in elastic‐plastic solids. I. Numerical simulations of plate acceleration Swegle, J. W.; Robinson, Allen C. Journal of Applied Physics, Vol. 66, Issue 7 https://doi.org/10.1063/1.344190	journal	October 1989
Numerical Investigation of the Stability of a Shock-Accelerated Interface between Two Fluids Meyer, K. A. Physics of Fluids, Vol. 15, Issue 5 https://doi.org/10.1063/1.1693980	journal	January 1972
Comparative study of viscoelastic properties using virgin yogurt Dimonte, Guy; Nelson, Don; Weaver, Sam Journal of Rheology, Vol. 42, Issue 4 https://doi.org/10.1122/1.550915	journal	July 1998
Turbulent Richtmyer–Meshkov instability experiments with strong radiatively driven shocks Dimonte, Guy; Schneider, Marilyn Physics of Plasmas, Vol. 4, Issue 12 https://doi.org/10.1063/1.872597	journal	December 1997
Supernova 1987A Arnett, W. David; Bahcall, John N.; Kirshner, Robert P. Annual Review of Astronomy and Astrophysics, Vol. 27, Issue 1 https://doi.org/10.1146/annurev.aa.27.090189.003213	journal	September 1989
Instability of accelerated elastic metal plates Plohr, B. J.; Sharp, D. H. Zeitschrift für angewandte Mathematik und Physik, Vol. 49, Issue 5 https://doi.org/10.1007/s000330050121	journal	January 1998
Simple model for the turbulent mixing width at an ablating surface Cherfils, Catherine; Mikaelian, Karnig O. Physics of Fluids, Vol. 8, Issue 2 https://doi.org/10.1063/1.868805	journal	February 1996
A numerical study of Richtmyer–Meshkov instability in continuously stratified fluids Pham, T.; Meiron, D. I. Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 2 https://doi.org/10.1063/1.858859	journal	February 1993
Three-dimensional simulations and analysis of the nonlinear stage of the Rayleigh-Taylor instability Hecht, J.; Ofer, D.; Alon, U. Laser and Particle Beams, Vol. 13, Issue 3 https://doi.org/10.1017/S026303460000954X	journal	September 1995
Observations and theory of the AMPTE magnetotail barium releases Bernhardt, P. A.; Roussel-Dupre, R. A.; Pongratz, M. B. Journal of Geophysical Research, Vol. 92, Issue A6 https://doi.org/10.1029/JA092iA06p05777	journal	January 1987
Rayleigh-Taylor Instability in Elastic-Plastic Materials Dimonte, Guy; Gore, Robert; Schneider, Marilyn Physical Review Letters, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevLett.80.1212	journal	February 1998
Study of three‐dimensional Rayleigh–Taylor instability in compressible fluids through level set method and parallel computation Li, X. L. Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 8 https://doi.org/10.1063/1.858816	journal	August 1993
The nonlinear breakup of a magnetic layer: instability to interchange modes Cattaneo, F.; Hughes, D. W. Journal of Fluid Mechanics, Vol. 196 https://doi.org/10.1017/S0022112088002721	journal	November 1988
Rayleigh–Taylor stability criteria for elastic-plastic solid plates and shells Ruden, E. L.; Bell, D. E. Journal of Applied Physics, Vol. 82, Issue 1 https://doi.org/10.1063/1.365795	journal	July 1997
A numerical study of bubble interactions in Rayleigh–Taylor instability for compressible fluids Glimm, J.; Li, X. L.; Menikoff, R. Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 11 https://doi.org/10.1063/1.857679	journal	November 1990
Experiments on the Richtmyer–Meshkov instability: Small‐scale perturbations on a plane interface Brouillette, M.; Sturtevant, B. Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 4 https://doi.org/10.1063/1.858637	journal	April 1993
Potential flow models of Rayleigh–Taylor and Richtmyer–Meshkov bubble fronts Hecht, Jacob; Alon, Uri; Shvarts, Dov Physics of Fluids, Vol. 6, Issue 12 https://doi.org/10.1063/1.868391	journal	December 1994
Radiation driven planar foil instability and mix experiments at the AWE HELEN laser Hansom, J. C. V.; Rosen, P. A.; Goldack, T. J. Laser and Particle Beams, Vol. 8, Issue 1-2 https://doi.org/10.1017/S0263034600007825	journal	January 1990
Nonlinear evolution of multimode Rayleigh–Taylor instability in two and three dimensions Shvarts, D.; Alon, U.; Ofer, D. Physics of Plasmas, Vol. 2, Issue 6 https://doi.org/10.1063/1.871476	journal	June 1995
Molecular mixing in Rayleigh–Taylor instability Linden, P. F.; Redondo, J. M.; Youngs, D. L. Journal of Fluid Mechanics, Vol. 265 https://doi.org/10.1017/S0022112094000777	journal	April 1994
Acceleration instability in elastic‐plastic solids. II. Analytical techniques Robinson, Allen C.; Swegle, J. W. Journal of Applied Physics, Vol. 66, Issue 7 https://doi.org/10.1063/1.344191	journal	October 1989
A simple experiment to investigate two‐dimensional mixing by Rayleigh–Taylor instability Andrews, M. J.; Spalding, D. B. Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 6 https://doi.org/10.1063/1.857652	journal	June 1990
Weakly nonlinear hydrodynamic instabilities in inertial fusion Haan, S. W. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 8 https://doi.org/10.1063/1.859603	journal	August 1991
Three‐dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability Youngs, David L. Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5 https://doi.org/10.1063/1.858059	journal	May 1991
Further experimentation on Taylor instability in solids Barnes, John F.; Janney, D. H.; London, Roger K. Journal of Applied Physics, Vol. 51, Issue 9 https://doi.org/10.1063/1.328339	journal	September 1980
Bubble competition in Rayleigh–Taylor instability Zufiria, Juan A. Physics of Fluids, Vol. 31, Issue 3 https://doi.org/10.1063/1.866825	journal	January 1988
Analytic theory of Richtmyer–Meshkov instability for the case of reflected rarefaction wave Velikovich, Alexander L. Physics of Fluids, Vol. 8, Issue 6 https://doi.org/10.1063/1.868938	journal	June 1996
Analytical Solutions of Layzer-Type Approach to Unstable Interfacial Fluid Mixing Zhang, Qiang Physical Review Letters, Vol. 81, Issue 16 https://doi.org/10.1103/PhysRevLett.81.3391	journal	October 1998
Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios Alon, U.; Hecht, J.; Ofer, D. Physical Review Letters, Vol. 74, Issue 4 https://doi.org/10.1103/PhysRevLett.74.534	journal	January 1995
Experimental investigation into inertial properties of Rayleigh–Taylor turbulence Kucherenko, Yu. A.; Balabin, S. I.; Cherret, R. Laser and Particle Beams, Vol. 15, Issue 1 https://doi.org/10.1017/S0263034600010715	journal	March 1997
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I Taylor, Geoffrey Ingram Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 201, Issue 1065, p. 192-196 https://doi.org/10.1098/rspa.1950.0052	journal	March 1950
Validation of the Sharp–Wheeler bubble merger model from experimental and computational data Glimm, J.; Li, X. L. Physics of Fluids, Vol. 31, Issue 8 https://doi.org/10.1063/1.866660	journal	January 1988
Molecular mixing in Rayleigh–Taylor instability. Part I: Global mixing Linden, P. F.; Redondo, J. M. Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5 https://doi.org/10.1063/1.858055	journal	May 1991
Experimental investigation of Richtmyer–Meshkov instability in shock tube Houas, L.; Chemouni, I. Physics of Fluids, Vol. 8, Issue 2 https://doi.org/10.1063/1.868845	journal	February 1996
On the Instability of Superposed Fluids in a Gravitational Field. Layzer, David The Astrophysical Journal, Vol. 122 https://doi.org/10.1086/146048	journal	July 1955
Rayleigh–Taylor stability for a normal shock wave–density discontinuity interaction Fraley, Gary Physics of Fluids, Vol. 29, Issue 2 https://doi.org/10.1063/1.865722	journal	January 1986
The intrusion of fluid mechanics into geology Huppert, Herbert E. Journal of Fluid Mechanics, Vol. 173 https://doi.org/10.1017/S0022112086001271	journal	December 1986
Hot, diamagnetic cavities upstream from the Earth's bow shock Thomsen, M. F.; Gosling, J. T.; Fuselier, S. A. Journal of Geophysical Research, Vol. 91, Issue A3 https://doi.org/10.1029/JA091iA03p02961	journal	January 1986
A linear electric motor to study turbulent hydrodynamics Dimonte, Guy; Morrison, Jim; Hulsey, Scott Review of Scientific Instruments, Vol. 67, Issue 1 https://doi.org/10.1063/1.1146585	journal	January 1996
Turbulent Rayleigh-Taylor instability experiments with variable acceleration Dimonte, Guy; Schneider, Marilyn Physical Review E, Vol. 54, Issue 4 https://doi.org/10.1103/PhysRevE.54.3740	journal	October 1996
Stability of plasmas confined by magnetic fields Rosenbluth, M. N.; Longmire, C. L. Annals of Physics, Vol. 1, Issue 2 https://doi.org/10.1016/0003-4916(57)90055-6	journal	May 1957
Instability of the interface of two gases accelerated by a shock wave Meshkov, E. E. Fluid Dynamics, Vol. 4, Issue 5 https://doi.org/10.1007/BF01015969	journal	January 1972

Similar Records

Nonlinear evolution of the Rayleigh{endash}Taylor and Richtmyer{endash}Meshkov instabilities

Journal Article · Sat May 01 00:00:00 EDT 1999 · Physics of Plasmas · OSTI ID:344935

Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios

Journal Article · Sun Jan 22 23:00:00 EST 1995 · Physical Review Letters; (United States) · OSTI ID:6544432

Oblique shocks and the combined Rayleigh--Taylor, Kelvin--Helmholtz, and Richtmyer--Meshkov instabilities

Journal Article · Wed Jun 01 00:00:00 EDT 1994 · Physics of Fluids; (United States) · OSTI ID:7281173

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Growth
Impact Shock
Instability
Mixing
Nonlinear Problems
Rayleigh-Taylor Instability

Nonlinear evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Citation Formats

References (62)

Similar Records

Related Subjects