Flows in a fluid layer induced by the combined action of a shear stress and the Soret effect

Convection in a horizontal fluid layer of a binary mixture is studied analytically and numerically. In the formulation of the problem, use is made of the Boussinesq approximation. Neumman boundary conditions are specified for the temperature on all walls of the cavity. In addition of the Soret contribution, a shear stress, τ, is applied on the upper free surface of the layer. The flows are found to be dependent of the Darcy–Rayleigh number, RT, the Lewis number, Le, the solutal to thermal buoyancy ratio, ϕ, the shear stress, τ and the thermal boundary conditions. Numerical results for finite amplitude convection, obtained by solving numerically the full governing equations, are found to be in good agreement with the analytical solution based on the parallel flow approach. For given sets of the control parameters, the occurrence of multiple steady state solutions is demonstrated. The existence of subcritical bifurcations for both stabilizing and destabilizing mass flux is also demonstrated.