Double-diffusive buoyancy convection in a square cuboid with horizontal temperature and concentration gradients

Abstract

Double-diffusive buoyancy convection in a three-dimensional (3D) square cuboid is studied in the present paper. Both the temperature and solute concentration gradients are applied horizontally. Direct numerical simulations are carried out for Rayleigh number 10≤Ra≤2×105, buoyancy ratio -2≤Rρ≤0, and Lewis number 2≤Le≤1000. Different front–rear symmetric solutions are found, and the flow structures are essentially three-dimensional. As each of the parameters is varied, typical pitchfork bifurcation is encountered, given appropriate disturbances. The resultant asymmetric solution presents a diagonal flow configuration. Different solution branches are denoted in terms of Nusselt and Sherwood numbers and corresponding two-dimensional (2D) model results are also presented to depict the deviations. In some parameter ranges, the 2D model significantly over-predicts the heat and mass transfer rates. More importantly, it fails to predict any unsteadiness of the flow, even when the corresponding 3D solution is chaotic. The onset of convection from the quiescent equilibrium state is also considered.