Statistical mechanics merger model for hydrodynamic instabilities

The nonlinear growth of the multimode Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities is treated by a similar statistical mechanics merger model, using bubbles as the elementary particle in the RM and RT instabilities and eddies in the KH instability. Two particle interaction is demonstrated and merger rates are calculated. Using a statistical merger model, the mixing front evolution scaling law is derived. For the RT bubble front height a scaling law of αAgt², with α ≅ 0.05, is derived. For the RM bubble front, a power law of t^0.4 is obtained for all Atwood numbers. For the KH case the mixing zone grows linearly with time through a mechanism of eddy merger. Good agreement with simulations and experiments is achieved.