Three-dimensional simulations of turbulent mixing in spherical implosions

Abstract

High-resolution large-eddy simulations of turbulent mixing at the inner surface of a dense shell which undergoes forced compression by a spherically imploding shock wave are presented. Perturbations on the inner surface grow as a result of Richtmyer-Meshkov and Rayleigh-Taylor instabilities and effects related to geometric convergence and compressibility. Three different cases with different initial surface perturbations, one broadband and two narrowband, are considered. The perturbation power spectrum is related to the mode number via Pℓ ∝ ℓn, where the case with broadband perturbations has n = −2, and modes in the range ℓ = 6–200. The narrowband perturbations have n = 0 and modes in the range ℓ = 50–100 and ℓ = 100–200. The simulations are carried out in spherical coordinates using the PLUTO hydrodynamics code. Results on the mix layer width, molecular mix, and turbulent kinetic energy distribution are presented, demonstrating clearly the impact of the amplitude and spectral form of the initial perturbation on the evolution of integral properties. A recently developed model predicting the growth of single mode perturbations in spherical implosions including shock waves is extended to predict mix layer amplitudes for broadband and narrowband cases, along with a model proposed by Mikaelian [“Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells,” Phys. Rev. A 42, 3400–3420 (1990)]. The resultant layer amplitude predictions from the new model are in good agreement with the numerical results while the longest wavelengths are not yet saturated, while Mikaelian’s model agrees well where the initial modes are saturated.