Quantitative theory of Richtmyer-Meshkov instability in three dimensions

A material interface between two fluids of different density accelerated by a shock wave is unstable. This instability is known as the Richtmyer-Meshkov instability. Previous theoretical and numerical studies of this instability primarily focused on fluids in two dimensions. In this paper, we present studies of the Richtmyer-Meshkov instability in three dimensions. There are three main new results presented here: (1) The analysis of the linear theory of the Richtmyer-Meshkov instability for both the reflected shock and reflected rarefaction wave cases. (2) Derivations of nonlinear perturbative solutions for an unstable interface between incompressible fluids (evaluated explicitly for the impulsive model through the third order). (3) A quantitative nonlinear theory of the compressible Richtmyer-Meshkov instability from early to later times. Our nonlinear theory contains no free parameter and provides analytical predictions for the overall growth rate, as well as the growth rates of bubble and spike, of Richtmyer-Meshkov unstable interfaces. Comparison to numerical simulations, which show excellent agreement to our theory, will be presented separately. © 1999 Birkhäuser Verlag, Basel