Rotating porous convection with prescribed heat flux

The problem of thermal convection in a rotating horizontal layer of porous medium is considered. The porous medium is described by the equations of Darcy. A novel aspect of this work is to consider boundary conditions for the temperature of Newton–Robin type with heat flux prescribed as a limiting case. The effect of rotation is found to be crucial. For the Taylor number small enough the critical wave number is zero but we find a threshold such that for Taylor numbers beyond this non-zero critical wave numbers are found. The threshold is verified via a weakly nonlinear analysis. Finally, a sharp global nonlinear stability analysis is given.