On the miscible Rayleigh-Taylor instability: two and three dimensions

We investigate the miscible Rayleigh-Taylor (RT) instability in both two an d three dimensions using direct numerical simulations, where the working fl uid is assumed incompressible under the Boussinesq approximation. We first consider the case of randomly perturbed interfaces. With a variety of diagn ostics, we develop a physical picture for the detailed temporal development of the mixed layer: we identify three distinct evolutionary phases in this development, which can be related to detailed variations in the growth of the mixing zone. Our analysis provides an explanation for the observed diff erences between two- and three-dimensional RT instability; the analysis als o leads us to concentrate on the RT models which (i) work equally well for both laminar and turbulent flows, and (ii) do not depend on turbulent scali ng within the mixing layer between fluids. These candidate RT models are ba sed on point sources within bubbles (or plumes) and their interaction with each other (or the background flow). With this motivation, we examine the e volution of single plumes, and relate our numerical results (for single plu mes) to a simple analytical model for plume evolution.