Layer Formation in Semiconvection

Abstract

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.