Layer formation in a thermally destabilized fluid with stable density
gradient has been observed in laboratory experiments and has been proposed as a
mechanism for mixing molecular weight in late stages of stellar evolution in
regions which are unstable to semiconvection. It is not yet known whether such
layers can exist in a very low viscosity fluid: this work undertakes to address
that question. Layering is simulated numerically both at high Prandtl number
(relevant to the laboratory) in order to describe the onset of layering
intability, and the astrophysically important case of low Prandtl number. It is
argued that the critical stability parameter for interfaces between layers, the
Richardson number, increases with decreasing Prandtl number. Throughout the
simulations the fluid has a tendency to form large scale flows in the first
convecting layer, but only at low Prandtl number do such structures have
dramatic consequences for layering. These flows are shown to drive large
interfacial waves whose breaking contributes to significant mixing across the
interface. An effective diffusion coefficient is determined from the simulation
and is shown to be much greater than the predictions of both an enhanced
diffusion model and one which specifically incorporates wave breaking. The
results further suggest that molecular weight gradient interfaces are
ineffective barriers to mixing even when specified as initial conditions, such
as would arise when a compositional gradient is redistributed by another
mechanism than buoyancy, such as rotation or internal waves
