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

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 $h_B={\alpha }_B\mathrm{Ag}{t}^2$ [$h_s={\alpha }_s\mathrm{}\left(A\right)g{t}^2$] with ${\alpha }_B=0.05\mathrm{}$, while Richtmyer-Meshkov bubble (spike) fronts are found as $h_B=a_B{t}^{{\theta }_B}$ ($h_s=a_s{t}^{{\theta }_s\mathrm{}\left(A\right)\mathrm{}}$) with ${\theta }_B=0.4\mathrm{}$ at all $A\text{'}\mathrm{s}$. The dependence of these scaling laws and parameters on $A$ and on initial conditions is explained.