Padé approximation to an interfacial fluid mixing problem

The material interface between two fluids of different densities is unstable under acceleration by a shock wave. This phenomenon is known as the Richtmyer-Meshkov instability. Theories have failed to provide quantitatively correct predictions for the growth rates of the unstable interface. Recently the authors have developed a quantitative theory based on the methods of Padé approximations and of asymptotic matching. In this letter, we extend our theory to the growth rates of the spike and bubble for the systems in two and three dimensions, and for systems with or without phase inversions. Our theoretical predictions are in excellent agreement with the results of full numerical simulations over the full time period from the initial linear (small amplitude) to moderately large amplitude nonlinear regimes.