Investigations Of Compressible Cylindrical Rayleigh-Taylor Instability And Turbulent Mixing

Rayleigh-Taylor(RT)instability occurs at a perturbed interface between two fluids when an external acceleration imposed points from the heavier to the lighter fluid.RT instability and its induced RT turbulence plays an important role in inertial confinement fusion(ICF)and supernova explosions.The evolution of RT instability is of crucial importance in designing capsules in ICF and is taken as a controlling factor in the rate of formation of heavy elements in supernova.In present study,direct numerical simulations and theoretical analysis methods are used to establish the analytical model of nonlinear evolution of single-mode RT instability in cylindrical geometry,present the scaling law of the mixing layer in cylindrical RT turbulence and investigate the compressibility effects on the kinetic energy and enstrophy transfer in compressible RT turbulence.The results and conclusions are briefly given as follows:(1)An analytical model of nonlinear evolution of two-dimensional single-mode RT instability in cylindrical geometry at arbitrary Atwood number is derived for the first time.Our model covers a full scenario of bubble evolution from the earlier exponential growth to the nonlinear regime with the bubbles growing in time as 1/2abt2 for cylindrical RT instability,other than as for planar RT instability,where ab and Vb are the bubble acceleration and velocity,respectively.The asymptotic solution of this model reveals that the nonlinear saturation of cylindrical RT instability behaves as an acceleration saturation and the saturating acceleration ab is formulated as a simplified function of the external acceleration,Atwood number and number of perturbation waves.This model can be reduced to that of the saturating bubble velocity of planar RT instability as the cylindrical geometry effect vanishes.This model's predictions are in good agreement with data from direct numerical simulations.(2)The nonlinear evolution of mixing layer in cylindrical RT turbulence is studied theoretically and numerically.The scaling law of the mixing layer in cylindrical RT turbulence is derived based on physical insights for the first time and verified by direct numerical simulation of the Navier-Stokes equations.Specifically,the outward mixing layer satisfies the hyperbolic cosine growth and the inward mixing layer obeys the cosine growth,respectively,in cylindrical geometry.It is inter-esting to note that the scaling laws for the cylindrical RT turbulence transcend the classical power law for the planar RT turbulence,but can be reduced to the quadratic growth when cylindrical geometry effect vanishes.Further,characteris-tic time and length scales are proposed by means of the scaling laws representing a general description of the self-similarly evolving features of mixing layer in the cylindrical RT turbulence.(3)Kinetic energy and enstrophy transfer in compressible RT turbulence were investi-gated by means of direct numerical simulation.It is revealed that compressibility plays an important role in the kinetic energy and enstrophy transfer based on analyses of the large-scale equations.For the generation and transfer of kinetic energy,some findings have been obtained as follows.The pressure-dilatation work dominates the generation of kinetic energy in the early stage of flow evolution.The baropycnal work and deformation work handle the kinetic energy transfer from large to small scales on average for RT turbulence.The baropycnal work is mainly responsible for the kinetic energy transfer on large scales,and the de-formation work for the kinetic energy transfer on small scales.The baropycnal work is also disclosed to be related to the compressibility from the finding that the expansion motion enhances the positive baropycnal work and the compression motion strengthens the negative baropycnal work.For the generation and trans-fer of enstrophy,the horizontal enstrophy is generated by the baroclinic effect and the vertical enstrophy by vortex stretching and tilting.Then the enstrophy is strengthened by the vortex stretching and tilting during the evolution of RT turbulence and the vorticity tends to be isotropic in the turbulent mixing region.The large-scale enstrophy equation in compressible flow has also been derived to deal with the enstrophy transfer.It is identified that the enstrophy is transferred from large to small scales on average and tends to stabilize for RT turbulence.