A numerical study of the statistics of a two-dimensional Rayleigh–Taylor mixing layer

A two-dimensional Rayleigh–Taylor mixing layer was numerically simulated to determine the growth rate of the mixing layer for an ensemble of initial conditions. The numerical algorithm used is a recently developed lattice Boltzmann method for multiphase flow. Small variations in the initial conditions of the fluid interface are observed to yield large variations in the growth rate of the mixing-layer width. Consequently, an ensemble of simulations has been generated to provide a statistical basis for determining the mixing-layer growth rate. The results for this ensemble indicate that the mixing-layer attains an approximate state of self-similarity and yields a distribution of mixing-layer growth rates.

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

[2]  Xiaolin Li.  A NUMERICAL STUDY OF THREE-DIMENSIONAL BUBBLE MERGER IN THE RAYLEIGH-TAYLOR INSTABILITY , 1996 .

[3]  Steven A. Orszag,et al.  Three-dimensional simulations and analysis of the nonlinear stage of the Rayleigh-Taylor instability , 1995 .

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

[5]  G. Taylor.  The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[6]  Raoyang Zhang,et al.  A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh-Taylor Instability , 1998 .

[7]  Marilyn Schneider,et al.  LARGE AND SMALL SCALE STRUCTURE IN RAYLEIGH-TAYLOR MIXING , 1998 .

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

[9]  David H. Sharp,et al.  Density dependence of Rayleigh–Taylor and Richtmyer–Meshkov mixing fronts , 2000 .

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

[11]  D. Youngs,et al.  Modelling turbulent mixing by Rayleigh-Taylor instability , 1989 .

[12]  M. J. Andrews,et al.  Turbulent mixing by Rayleigh-Taylor instability , 1986 .

[13]  Shiyi Chen,et al.  On the three-dimensional Rayleigh–Taylor instability , 1999 .

[14]  Serge Gauthier,et al.  A k‐ε model for turbulent mixing in shock‐tube flows induced by Rayleigh–Taylor instability , 1990 .

[15]  P. Littlewood.  Metastability and nonlinear dynamics of sliding charge density waves , 1986 .

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

[17]  Qiang Zhang,et al.  A numerical study of bubble interactions in Rayleigh–Taylor instability for compressible fluids , 1990 .

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

[19]  G. Doolen,et al.  Comparison of the Lattice Boltzmann Method and the Artificial Compressibility Method for Navier-Stokes Equations , 2002 .

[20]  Qiang Zhang,et al.  A two‐phase flow model of the Rayleigh–Taylor mixing zone , 1996 .