An Analytical Nonlinear Theory of Richtmyer- Meshkov Instability

Richtmyer-Meshkov instability is a fingering instability which occurs at a material interface accelerated by a shock wave. We present an analytic, explicit prediction for the growth rate of the unstable interface. The theoretical prediction agrees, for the first time, with the experimental data on air-SF6, and is in remarkable agreement with the results of recent full non-linear numerical simulations from early to late times. Previous theoretical predictions of the growth rate for air-SF6 unstable interfaces were about two times larger than the experimental data. PACS numbers: 47.20.Ma, 47.20.Ky A material interface between two fluids of different density accelerated by a shock wave is unstable. This instability is known as Richtmyer-Meshkov (RM) instability. It plays an important role in studies of supernova and inertial confinement fusion (ICF). The occurrence of this instability was first predicted theoretically by Richtmyer [1] in 1960, and ten years later, confirmed experimentally by Meshkov [2]. Since then several experiments [3-4] and numerical simulations [5-11] on the growth of the RM unstable interfaces have been performed. Several theories have been developed by different approaches [1,12-15]. Most of previous theoretical work focused on the asymptotic growth rate of the linearized Euler equations. However, the growth of the RM unstable interface is nonlinear and so far theories failed to give a quantitatively correct prediction for the growth rate of RM unstable interface in the nonlinear regime. Previous theoretical predictions were about twice as large as the experimental data on air-Sf6 . In this paper, we present a non-linear theory for Richtmyer-Meshkov instability for compressible fluids in the case when the reflected wave is a shock. Our result is analytic and