Stochastic modeling of statistically unsteady processes

Abstract

We develop a stochastic model describing Rayleigh–Taylor (RT) turbulent mixing with uniform and non-uniform accelerations. The process is statistically unsteady, so that the mean values of the flow quantities vary with time, and there are also time-dependent fluctuations around these means. The randomness of the dissipation process in RT mixing is accounted for with a set of stochastic nonlinear differential equations with multiplicative noise. An extensive study of the parameter regime is conducted. We show that for power-law asymptotic solutions describing the mixing process the exponent is relatively insensitive and the pre-factor is sensitive to fluctuations. The statistically unsteady process has an invariant measure. For uniform and non-uniform accelerations, with and without turbulent diffusion accounted for, the ratio between the rates of loss and gain of specific momentum is the statistically steady value.