Analytical nonlinear theory of unstable fluid mixing driven by a shock wave.

摘要

e 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 unstable interface between fluids of arbitrary density ratios in two and three dimensions.;The mathematical techniques which we used in our theoretical formulation are a systematic nonlinear perturbation expansions, Pade approximation and the asymptotic matching. Our validation study shows that these techniques have been successfully applied to predict the growth rates of the unstable interface.;Our theory contains no adjustable parameters. The theoretical predictions of our nonlinear theory are are in excellent agreements with results of full nonlinear numerical simulations and the experimental data in two dimensions from the linear (small amplitude) to the nonlinear regimes. The predictions of linear theories are qualitatively incorrect at late times. Our theory has identified that the RM unstable system goes through a transition from a compressible and linear one at early times to a nonlinear and incompressible one at later times.;The nonlinear theory has been extended to fluids in three dimensions. Our results show that the growth rates for different orientation angle