Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios

Abstract

The nonlinear evolution of large structure in Rayleigh-Taylor and Richtmyer-Meshkov bubble and spike fronts is studied numerically and explained theoretically on the basis of single-mode and two-bubble interaction physics at Atwood numbers ($A$). Multimode Rayleigh-Taylor bubble (spike) fronts are found as ${h}_{B}={\ensuremath{\alpha}}_{B}\mathrm{Ag}{t}^{2}$ [${h}_{s}={\ensuremath{\alpha}}_{s}(A)g{t}^{2}$] with ${\ensuremath{\alpha}}_{B}=0.05$, while Richtmyer-Meshkov bubble (spike) fronts are found as ${h}_{B}={a}_{B}{t}^{{\ensuremath{\theta}}_{B}}$ (${h}_{s}={a}_{s}{t}^{{\ensuremath{\theta}}_{s}(A)}$) with ${\ensuremath{\theta}}_{B}=0.4$ at all $A'\mathrm{s}$. The dependence of these scaling laws and parameters on $A$ and on initial conditions is explained.