On the stability of thermosolutal rotating porous convection subject to a lack of thermal equilibrium

This paper investigates the linear and weakly nonlinear stability of thermosolutal rotating porous convection subject to a lack of thermal equilibrium. Being an example of a triply diffusive fluid system in porous media with multiparameters, some novel results on the linear instability are delineated for a few isolated cases. The otherwise stabilizing factors such as stabilizing solute concentration and rotation are shown to destabilize the system under certain parameters space. Besides, the existence of a completely detached closed convex oscillatory neutral curve from that of the stationary neutral curve is uncovered indicating the requirement of three critical thermal Darcy-Rayleigh numbers to identify the linear instability criteria instead of the usual single critical value. The multivalued nature of the stability boundaries for the case of completely detached oscillatory neutral curves is displayed. The co-dimension-2 points are found through a stability map with the demarcation of stationary and oscillatory convective regions in a plane of Darcy-Taylor and scaled Vadasz numbers. Weakly nonlinear stability theory is carried out for a stationary case by using a modified multi-scale method and thereby the complex Ginzburg-Landau amplitude equation is derived identifying the pitchfork bifurcation. Moreover, heat and mass transport are quantified in terms of average thermal and solute Nusselt numbers, respectively.