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 A --> 0) is treated by the motion of point potential vortices. The dynamics of a periodic bubb le array and the competition between bubbles of different sizes is analyzed . A statistical mechanics model for the multimode front mixing evolution, s imilar to the single-bubble growth and two-bubble interaction based model u sed by Alon et al. [Phys. Rev. Lett. 72, 2867 (1994)] for A = 1, is present ed. Using the statistical bubble merger model, a power law of t(0.4) for th e mixing zone growth is obtained, similar to that of the bubble front growt h for the A = 1 case and in good agreement with experiments and full numeri cal simulations. [S1063-651X(98)13312-3].