Layer mergers in Oscillatory Double-Diffusive Convection

Oscillatory double-diffusive convection (ODDC) occurs in the interiors of planets and stars with a stabilizing composition gradient and a destabilizing temperature gradient. The results of previous studies in triply periodic DNS at low Prandt numbers have shown that regions of the fluid subject to ODDC spontaneously form convective layers that merge over time. These results were confirmed under fixed-flux boundary conditions. As a result of the layer mergers, the initially stable regions in the simulated domain ultimately become fully convective. It is, therefore, essential to understand the physics of the layer coarsening process. Radko (2007) demonstrated that two distinct merger processes exist, namely interface erosion and layer growth. We propose simple models for each of these merger types in the context of ODDC and compare them successfully with the DNS. This enables us to predict the lifetime of the diffusive staircases in planets and stars.