We investigate the miscible Rayleigh–Taylor (RT) instability in both two and three
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 this development, 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 (i) work equally well for
both laminar and turbulent flows, and (ii) 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 their interaction with each other (or the background
flow). With this motivation, we examine the evolution of single plumes, and relate our
numerical results (for single plumes) to a simple analytical model for plume evolution.