Analytical Nonlinear Theory of Unstable Fluid Mixing Driven by a Shock Wave

We present a nonlinear theory of the growth of fingers at interface between two fluids of different densities driven by a shock wave. This interfacial instability is known as the Richtmyer-Meshkov (RM) instability. Previous theoretical work focused on linear regime and failed to give a quantitatively correct prediction for the growth rate of Richtmyer-Meshkov unstable interface in the nonlinear regime. Spikes and bubbles are formed at the unstable interface. A spike (bubble) is a portion of heavy (light) fluid penetrating into light (heavy) fluid. The theory presented in this dissertation provides analytical, explicit expressions for quantitative predictions of the overall growth rate as well as the growth rate of the spike and bubble of the untable interface between fluids of arbitrary..