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

Abstract

Via the auxiliary system method (Rionero, 2012 [35] and Rionero, 2013 [36,37]) 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 T and Vadasz number Va (Section 2). For the tridimensional perturbations and the full non-linear problem, it is shown that:(a)there exists a critical Taylor number Tc≈1.53 such that for T≤Tc the inertia has no effect on the onset of convection;(b)for T>Tc there exists an associate critical Vadasz number Va(c)(T)(>0) such that, only for Va<Va(c)(T), the inertia has effect on the onset of convection, and only in this case the convection arises via an oscillatory motion (cf. Theorems 5.2 and 5.3);(c)subcritical instabilities do not exist;(d)the global non-linear stability is guaranteed by the linear stability;(e)also in the case {T>Tc, Va<Va(c)} the critical Rayleigh number can be given in closed form.