An Appropriate Metric to Switch on a Turbulence Model for Rayleigh-Taylor Instability Driven Mixing

Abstract

Rayleigh-Taylor (RT) instability occurs at a perturbed interface between fluids of different densities, when the lighter fluid is accelerated into the heavier fluid (∇p · ∇ρ < 0, where p is pressure, and ρ is density). In time, as the two fluids seek to reduce their combined potential energy, the mixing becomes turbulent. This fundamental instability is observed, and plays a key role, in numerous natural phenomena, e.g. supernovae explosions, and in engineering applications, e.g. Inertial Confinement Fusion (ICF). The importance of initial condition (ICs) effects on the growth and mixing of Rayleigh-Taylor instability open an opportunity for “design” of RT turbulence for engineering, and question our current predictive capability. Indeed, commonly used turbulence models used for engineering applications are tuned for fully developed turbulence, whereas RT instability is a dynamic process that evolves toward turbulence under the influence of ICs. Therefore, our efforts aim at defining a procedure for properly accounting for initial conditions in variable density (RT) turbulence models. Our strategy is to have a model for the “early” evolution of the RT instability that will produce the initial conditions for the turbulence model. We already dispose of a modal model to evolve the RT mixing layer starting from almost any initial conditions. The present work is a first look at determining an appropriate metric for switching from the modal model to a variable density turbulence model.