  We investigate the miscible Rayleigh-Taylor (RT) instability in both 2 and 3
dimensions using direct numerical simulations, where the working fluid is
assumed incompressible under the Boussinesq approximation. We first consider
the case of randomly perturbed interfaces. With a variety of diagnostics, we
develop a physical picture for the detailed temporal development of the mixed
layer: We identify three distinct evolutionary phases in the development of the
mixed layer, which can be related to detailed variations in the growth of the
mixing zone. Our analysis provides an explanation for the observed differences
between two and three-dimensional RT instability; the analysis also leads us to
concentrate on the RT models which (1) work equally well for both laminar and
turbulent flows, and (2) do not depend on turbulent scaling within the mixing
layer between fluids. These candidate RT models are based on point sources
within bubbles (or plumes) and interaction with each other (or the background
flow). With this motivation, we examine the evolution of single plumes, and
relate our numerical results (of single plumes) to a simple analytical model
for plume evolution.
