Convection and stability in a rotating porous layer with alternating direction of the centrifugal body force

Abstract

An alternating direction of the centrifugal body force results when the axis of rotation is placed within the boundaries of a rotating fluid saturated porous layer. The onset of thermal convection and stability in a fluid saturated porous layer prevailing such conditions is investigated analytically. The marginal stability criterion was evaluated in terms of a critical centrifugal Rayleigh number and a corresponding critical wave number. The effect of the offset distance of the layer's cold wall from the axis of rotation on the convection is analyzed, showing that the critical centrifugal Rayleigh and wave numbers increase significantly as the layer's cold wall moves away from the rotation axis. This leads eventually to unconditional stability when the layer's hot wall coincides with the rotation axis. This unconditional stability prevails when the axis of rotation moves away from the porous domain, so that the imposed temperature gradient opposes the direction of the centrifugal acceleration. Significant effects on the convection pattern are identified as a result of the rotation axis location.