A Quantitative Theory of Richtmyer-Meshkov Instability in Compressible Fluids

Abstract

Richtmyer-Meshkov instability is a classical problem in mathematics, physics and engineering. This instability occurs upon a shock wave hitting a perturbed material interface between two different fluids. After the passage of the shock wave, the perturbation at the interface starts to grow and form nonlinear fingers. The intrinsical compressibility and nonlinearity make theoretical treatment of Richtmyer-Meshkov instability challenging, especially the treatment valid over all times. At early times the compressibility in this problem is of great importance and the Richtmyer-Meshkov unstable system is governed by the linearized Euler equations. As time evolves, the nonlinearity of the instability growth comes into play a significant role and thus the system is governed by the nonlinear equations. In this thesis, a quantitative theory is presented to predict the growth rates and amplitudes of fingers in Richtmyer-Meshkov instability for compressible fluids based on the methods of two-point Padé approximation and asymptotic matching. The quantitative theory developed in this thesis covers the entire time domain from early to late times, and is applicable to systems with arbitrary fluid density ratios. A careful theoretical analysis is conducted to eliminate the possibilities of non-physical solutions and singularities. The quantitative theory is valid for both reflected shock wave and reflected rarefaction wave cases. The theoretical predictions are in good agreement with data from several independent numerical simulations and experiments.
In addition, attributing to the essential role that plays in the construction of compressible nonlinear theory, a compressible linear theory of Richtmyer-Meshkov instability in cylindrical tubes is formulated. It is also found that the growth rate and the amplitude of Richtmyer-Meshkov instability for different modes in cylindrical tubes satisfy a nice scaling law. It is shown that the linear theory in cylindrical tubes can be mapped to that in two dimensions through a proper scaling. Therefore, the theoretical analysis conducted for the two-dimensional linear theory also holds for the linear theory in cylindrical tubes.

Date of Award	7 Aug 2017
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Qiang ZHANG (Supervisor)