Oscillation phenomena in a thermohaline double-diffusive convection system

The incompressible, double-diffusive convection has been simulated using finite difference schemes. The Navier-Stokes equations are expressed in terms of stream function and vorticity. Because of the existence of large velocity, temperature and salinity gradients in boundary layers, a simple coordinate transformation is used to concentrate the grid points near the wall. The finite difference methods used include the high-order accurate upwind difference scheme. It is shown that the scheme is a good candidate for direct simulations of double-diffusive convection flows. The boundary-fitted coordinate is used so that finer grids can be used to resolve the flow in the boundary layers. The proposed method is first applied to the symmetric states of a salinity-dominated flow with Rρ = 1.68 and a temperature-dominated flow with Rρ = 0.32. The numerical results agree well with those by Quon & Ghil(1992 J. Fluid Mech. 245 449). Then our work concentrates on the study of the flow characteristic of the two-dimensional thermosolutal equilibrant regime for different Lewis numbers. It can be found that there are several different states in this system, which could be the symmetric states, the periodic oscillations or non-periodic (random) states.