Saline groundwater and irrigation drainage are commonly diverted and stored in both natural and artificial depressions throughout the Murray-Darling Basin of Australia. The disposal basin brines that are formed am often denser than ambient groundwater. Under certain conditions these dense brines may become unstable causing them to mix with groundwater over distances several orders of magnitude greater than due to diffusion alone. A model is developed to study the mixed convection processes below a saline disposal basin located between a recharge and discharge zone. Numerical simulations are performed in cross-section using the 2-D density dependent model SUTRA (saturated-unsaturated transport). It is shown that the salt front movement is related to both the ability of the dense saline brines to mix convectively with underlying groundwaters (Rayleigh convection) and the strength of the regional advective velocity. Both homogeneous and heterogeneous aquifer systems are studied and the effects of anisotropy are considered. Our numerical results suggest that the behaviour of a dense brine plume overlying less dense groundwater in a homogeneous porous medium depends on the magnitude of at least two non-dimensional numbers, a Rayleigh number and modified Peclet number, defined in terms of basin scale hydrogeologic parameters including dispersion. It is shown that the onset of gravitational instabilities and the formation of free convective cells begins when the magnitude of a non-dimensional parameter combining the Rayleigh and modified Peclet number exceeds a certain critical value.