Coriolis effect on gravity-driven convection in a rotating porous layer heated from below

Linear stability and weak nonlinear theories are used to investigate analyt ically the Coriolis effect on three-dimensional gravity-driven convection i n a rotating porous layer heated from below. Major differences as well as s imilarities with the corresponding problem in pure fluids (non-porous domai ns) are particularly highlighted. As such, it is found that, in contrast to the problem in pure fluids, overstable convection in porous media is not l imited to a particular domain of Prandtl number values (in pure fluids the necessary condition is Pr < 1). Moreover, it is also established that in th e porous-media problem the critical wavenumber in the plane containing the streamlines for stationary convection is not identical to the critical wave number associated with convection without rotation, and is therefore not in dependent of rotation, a result which is quite distinct from the correspond ing pure-fluids problem. Nevertheless it is evident that in porous media, j ust as in the case of pure fluids subject to rotation and heated from below , the viscosity at high rotation rates has a destabilizing effect on the on set of stationary convection, i.e. the higher the viscosity the less stable the fluid. Finite-amplitude results obtained by using a weak nonlinear ana lysis provide differential equations for the amplitude, corresponding to bo th stationary and overstable convection. These amplitude equations permit o ne to identify from the post-transient conditions that the fluid is subject to a pitchfork bifurcation in the stationary convection case and to a Hopf bifurcation associated with the overstable convection. Heat transfer resul ts were evaluated from the amplitude solution and are presented in terms of Nusselt number for both stationary and overstable convection. They show th at rotation has in general a retarding effect on convective heat transfer, except for a narrow region of small values of the parameter containing the Prandtl number where rotation enhances the heat transfer associated with ov erstable convection.