The Coriolis effect and travelling waves in porous media convection subject to rotation.

Abstract

This study intends to recover and expand the analytical work of Vadasz (1998) for linear and weak non-linear stability of a rotating porous media heated form below and subject to gravity and Conolis forces. It is shown that the viscosity has a destabilising effect at high rotation rate. It has been established that the critical wave number in a plane containing the streamlines is dependent on rotation. Finite amplitude calculations provide a set of differential equations for the amplitude and phase, corresponding to the stationary and over-stable convection, identifying the post-transient conditions that a fluid is subject to, i.e. a pitchfork bifurcation for the stationary case, or a Hopf bifurcation in the case of over-stable convection. The previous model (Vadasz [1998]) was extended with an additional time scale in order to represent amplitude fluctuations and a short space scale to include horizontal modes of oscillations. When the complete solution for the stream function or temperature is analysed, where left and right travelling waves are considered, we obtain a set of differential equations for the amplitude and phase. The solutions are discussed in this context.