Inertia effect on the onset of convection in rotating porous layers via the "auxiliary system method"

Via the auxiliary system method introduced by Rionero the onset of convection in rotating porous layers in the presence of inertia is investigated. The effects of rotation and inertia are respectively measured through the Taylor number and Vadasz number. For the tridimensional perturbations and the full nonlinear problem, it is shown that: there exists a critical Taylor below which the inertia has no effect on the onset of convection; for Taylor number greater of the critical Taylor number there exists an associate critical Vadasz number below which the inertia has effect on the onset of convection, and only in this case the convection arises via an oscillatory motion; subcritical instabilities do not exist; the global nonlinear stability is guaranteed by the linear stability.