Progress in understanding turbulent mixing induced by Rayleigh–Taylor and Richtmyer–Meshkov instabilities

Turbulent hydrodynamic mixing induced by the Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities occurs in settings as varied as exploding stars (supernovae), inertial confinement fusion (ICF) capsule implosions, and macroscopic flows in fluid dynamics facilities such as shock tubes. Turbulence theory and modeling have been applied to RT and RM induced flows and developed into a quantitative description of turbulence from the onset to the asymptotic end-state. The treatment, based on a combined approach of theory, direct numerical simulation (DNS), and experimental data analysis, has broad generality. Three areas of progress will be reported. First, a robust, easy to apply criteria will be reported for the mixing transition in a time-dependent flow. This allows an assessment of whether flows, be they from supernova explosions or ICF experiments, should be mixed down to the molecular scale or not. Second, through DNS, the structure, scaling, and spectral evolution of the RT instability induced fl...

[1]  Dean Young.  First Course In Turbulence , 1999 .

[2]  Richard C. Miake-Lye,et al.  Structure and dynamics of round turbulent jets , 1983 .

[3]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[4]  Marilyn Schneider,et al.  Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories , 2000 .

[5]  R. P. Drake,et al.  The time scale for the transition to turbulence in a high Reynolds number, accelerated flow , 2003 .

[6]  P. Dimotakis.  The mixing transition in turbulent flows , 2000, Journal of Fluid Mechanics.

[7]  A. Cook,et al.  Energy transfer in Rayleigh-Taylor instability. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  K. I. Read,et al.  Experimental investigation of turbulent mixing by Rayleigh-Taylor instability , 1984 .

[9]  Hideaki Takabe,et al.  A review of astrophysics experiments on intense lasers , 2000 .

[10]  Roland Schiestel,et al.  Multiple‐time‐scale modeling of turbulent flows in one‐point closures , 1987 .

[11]  J. Clérouin,et al.  The viscosity of dense plasmas mixtures , 1998 .

[12]  J. Huba.  NRL: Plasma Formulary , 2004 .

[13]  Lord Rayleigh,et al.  LXXXII. On the motion of solid bodies through viscous liquid , 1911 .

[14]  Paul E. Dimotakis,et al.  Transition stages of Rayleigh–Taylor instability between miscible fluids , 2000, Journal of Fluid Mechanics.

[15]  P. Yeung,et al.  Numerical study of rotating turbulence with external forcing , 1998 .

[16]  H. Robey,et al.  Onset of turbulence in accelerated high-Reynolds-number flow. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  H. Wilhelmsson,et al.  Review of plasma physics: Vol. 1 (ed. M. A. Leontovich, Consultants Bureau, New York, 1965) pp. 326, $ 12.50 , 1966 .

[18]  Bradford Sturtevant,et al.  Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface , 1995 .

[19]  Ye Zhou,et al.  Formulation of a two-scale transport scheme for the turbulent mix induced by Rayleigh-Taylor and Richtmyer-Meshkov instabilities. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Ye Zhou.  A PHENOMENOLOGICAL TREATMENT OF ROTATING TURBULENCE , 1995 .

[21]  Dean R. Chapman,et al.  Computational Aerodynamics Development and Outlook , 1979 .

[22]  M. Brouillette.  THE RICHTMYER-MESHKOV INSTABILITY , 2002 .

[23]  W. Matthaeus,et al.  Extended inertial range phenomenology of magnetohydrodynamic turbulence , 1989 .

[24]  G. Batchelor,et al.  The theory of homogeneous turbulence , 1954 .

[25]  H. Schlichting.  Boundary Layer Theory , 1955 .

[26]  Ye Zhou.  Interacting scales and energy transfer in isotropic turbulence , 1993 .

[27]  D. Youngs,et al.  Numerical simulation of turbulent mixing by Rayleigh-Taylor instability , 1984 .

[28]  Peter Vorobieff,et al.  Experimental observations of the mixing transition in a shock-accelerated gas curtain , 1999 .

[29]  Manoochehr Koochesfahani,et al.  Mixing and chemical reactions in a turbulent liquid mixing layer , 1986, Journal of Fluid Mechanics.

[30]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[31]  R. P. Drake,et al.  Similarity Criteria for the Laboratory Simulation of Supernova Hydrodynamics , 1999 .

[32]  C. G. Speziale,et al.  Advances in the Fundamental Aspects of Turbulence: Energy Transfer, Interacting Scales, and Self-Preservation in Isotropic Decay , 1998 .

[33]  W. Cabot,et al.  Computing turbulent flows driven by Rayleigh-Taylor and Richtmyer-Meshkov instabilities , 2003 .

[34]  Ye Zhou,et al.  A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities , 2001 .

[35]  Charles G. Speziale,et al.  ANALYTICAL METHODS FOR THE DEVELOPMENT OF REYNOLDS-STRESS CLOSURES IN TURBULENCE , 1990 .

[36]  James Glimm,et al.  Experiments to Produce a Hydrodynamically Unstable, Spherically Diverging System of Relevance to Instabilities in Supernovae , 2002 .