Exploration of anisotropy on nonlinear stability of thermohaline viscoelastic porous convection

The nonlinear stability of thermohaline convection in a horizontal layer of an anisotropic porous medium saturated with an Oldroyd-B fluid is studied using a modified perturbation method. Anisotropy in permeability, thermal and solute diffusivities is modelled as second-rank tensors. The cubic Landau equations for steady and oscillatory bifurcating solutions are derived. It is apparent that subcritical instability is possible depending on the choices of governing parameters indicating the linear stability theory is not sufficient to capture the onset of convection. The effect of strain retardation parameter, solute Darcy-Rayleigh number, thermal anisotropy parameter as well as solute anisotropy parameter is to delay, while the effect of stress relaxation parameter, Lewis number and the mechanical anisotropy parameter is to hasten the onset of oscillatory convection. It is found that the stationary bifurcating solution is subcritical while that of oscillatory is supercritical at higher values of solute Darcy-Rayleigh number. The results of Maxwell fluid are obtained as a limiting case. Heat and mass transports are estimated using Nusselt number and Sherwood number, respectively and by tuning the anisotropy parameters it is possible to control the same.