Double-diffusive convection with fixed flux boundary conditions

Oscillatory double-diffusive convection occurs in planetary and stellar interiors that have a stabilizing composition gradient and a destabilizing temperature gradient. The nonlinear dynamics of this instability have been previously studied using triply periodic DNS which showed that the stratification spontaneously forms density layers that gradually merge over time. However, this model setup is somewhat unrealistic because it allows both heat and compositional fluxes through the domain to adjust to the evolving dynamics. By contrast, in planets and stars it is controlled by nuclear reaction rates and/or surface cooling. In this work, therefore, we study double-diffusive convection with fixed-flux boundary conditions for low Prandtl number. We use Dedalus, an open-source library for solving differential equations with spectral methods, to implement the model. Our simulations typically evolve through multiple phases: oscillatory double-diffusive convection, emergence of convective boundary layers and their growth, layer interface erosion, and fully convective phase. We propose simple models to describe the evolution of the system in each phase.