Vortex model for the nonlinear evolution of the multimode Richtmyer-Meshkov instability at low Atwood numbers

The nonlinear growth of the multimode Richtmyer-Meshkov instability in the limit of two fluids of similar densities (Atwood number →A0) is treated by the motion of point potential vortices. The dynamics of a periodic bubble array and the competition between bubbles of different sizes is analyzed. A statistical mechanics model for the multimode front mixing evolution, similar to the single-bubble growth and two-bubble interaction based model used by Alon et al. [Phys. Rev. Lett. 72, 2867 (1994)] for $A=1,$ is presented. Using the statistical bubble merger model, a power law of t0.4 for the mixing zone growth is obtained, similar to that of the bubble front growth for the $A=1$ case and in good agreement with experiments and full numerical simulations.