Numerical simulation of double-diffusive convection in a rectangular box

We directly simulate incompressible, double-diffusive convection in a vertical slot using a two-dimensional pseudospectral code. Incompressibility is achieved in our code by the consistent implementation of the tau correction. We find that layer dynamics depends on the particulars of the imposed boundary conditions for the temperature at the sidewalls and the density stratification ratio (the relative strength of the stabilizing solute gradient to the destabilizing horizontal thermal difference). We demonstrate the effects of the density stratification ratio on the layer dynamics by adopting three stratification ratios for the constant sidewall temperature case. We perform one simulation for constant lateral heat flux to study the effects of the temperature boundary conditions. We apply the argument for layering in turbulent stratified fluids to our problem, and find-despite the tilted nature of cell boundaries in our case-similarities in both the averaged equations and actual layer evolution. Finally, we provide details for both edge mergers and interior mergers.