Three-dimensional simulations and analysis of the nonlinear stage of the Rayleigh-Taylor instability

The nonlinear stage in the growth of the Rayleigh-Taylor instability in three dimensions (3D) is studied using a 3D multimaterial hydrodynamic code. The growth of a single classical 3D square and rectangular modes is compared to the growth in planar and cylindrical geometries and found to be close to the corresponding cylindrical mode, which is in agreement with a new Layzer-type model for 3D bubble growth. The Atwood number effect on the final shape of the instability is demonstrated. Calculations in spherical geometry of the late deceleration stage of a typical ICF pellet have been performed. The different late time shapes obtained are shown to be a result of the initial conditions and the high Atwood number. Finally, preliminary results of calculations of two-mode coupling and random perturbations growth in 3D are presented.

[1]  S. Orszag,et al.  Mode coupling in nonlinear Rayleigh–Taylor instability , 1992 .

[2]  Town,et al.  Three-dimensional simulations of the implosion of inertial confinement fusion targets. , 1991, Physical review letters.

[3]  Alon,et al.  Scale-invariant regime in Rayleigh-Taylor bubble-front dynamics. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  U. Alon,et al.  Potential flow models of Rayleigh–Taylor and Richtmyer–Meshkov bubble fronts , 1994 .

[5]  Gretar Tryggvason,et al.  Computations of three‐dimensional Rayleigh–Taylor instability , 1990 .

[6]  G. Pert,et al.  Non-linear Rayleigh-Taylor instability in (spherical) laser accelerated targets , 1987 .

[7]  John Lindl,et al.  Progress toward Ignition and Burn Propagation in Inertial Confinement Fusion , 1992 .

[8]  I. Catton,et al.  Three-dimensional Rayleigh-Taylor instability Part 1. Weakly nonlinear theory , 1988, Journal of Fluid Mechanics.

[9]  Advances in compressible turbulent mixing , 1992 .

[10]  G. Doolen,et al.  The effect of shape in the three-dimensional ablative Rayleigh-Taylor instability. I: Single-mode perturbations , 1993 .

[11]  K. W. Morton,et al.  Numerical methods for fluid dynamics , 1987 .

[12]  D. Layzer,et al.  On the Instability of Superposed Fluids in a Gravitational Field. , 1955 .

[13]  E. Ott,et al.  Three‐dimensional, nonlinear evolution of the Rayleigh–Taylor instability of a thin layer , 1984 .

[14]  Gardner,et al.  Ablative Rayleigh-Taylor instability in three dimensions. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[15]  Steven A. Orszag,et al.  Two‐phase flow analysis of self‐similar turbulent mixing by Rayleigh–Taylor instability , 1991 .

[16]  Yabe,et al.  Two- and three-dimensional behavior of Rayleigh-Taylor and Kelvin-Helmholtz instabilities. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[17]  Nishihara,et al.  Three-dimensional Rayleigh-Taylor instability of spherical systems. , 1990, Physical review letters.

[18]  Hecht,et al.  Scale invariant mixing rates of hydrodynamically unstable interfaces. , 1994, Physical review letters.

[19]  D. Youngs,et al.  Three-dimensional numerical simulation of turbulent mixing by Rayleigh-Taylor instability , 1991 .

[20]  R. Town,et al.  Three-dimensional simulations of the Rayleigh–Taylor instability during the deceleration phase , 1994 .