Introduction

Rayleigh–Taylor (RT) instability (see Sharp 1984) occurs when the interface between two fluids of different density is subjected to a normal pressure gradient with a direction such that the pressure is higher in the less dense fluid. The related Richtmyer–Meshkov (RM) process (see Holmes et al. 1999) occurs when a shock wave passes through a perturbed interface. These instabilities are currently of concern for researchers involved in inertial confinement fusion (ICF). RT and RM instabilities can degrade the performance of ICF capsules, where high-density shells are decelerated by lower-density thermonuclear fuel. In these applications and in many RT or RM laboratory experiments, the Reynolds number is very high. Turbulent mixing will then occur. Direct numerical simulation (DNS) is feasible at a moderate Reynolds number. However, for most experimental situations, the calculation of the evolution of turbulent mixing requires some form of large eddy simulation (LES).

The flows of interest here involve shocks and density discontinuities. It is then highly desirable to use monotonic or total variation diminishing (TVD) numerical methods, either for calculating the mean flow or the development of instabilities. Hence, for three-dimensional turbulent flows, monotone-integrated LES (MILES) is very strongly favored.

My purpose in this chapter is to show that a particular form of MILES gives good results for RT and RM mixing. I consider the mixing of miscible fluids, and I assume the Reynolds number to be high enough for the effect of the Schmidt number to be unimportant.