Centrifugal buoyancy in a rotating fluid layer next to and distant from the rotation axis

Abstract

An analytical investigation of the stability and onset of natural convection in a rotating fluid layer subject to a centrifugal body force and placed an arbitrary offset distance from the axis of rotation is presented. Linear stability as well as weak nonlinear analyses is performed to demonstrate the effect of centrifugal buoyancy. In the limit of an infinite distance from the center of rotation, the results are identical to the natural convection resulting from heating a fluid layer from below subject to the gravitational body force. The results provide the stability map for all non-negative values of the parameter controlling the offset distance from the axis of rotation. A clear break of symmetry results from the centrifugal buoyancy if the offset distance from the axis of rotation is not too large. The weak nonlinear solutions produce amplitudes for the convection velocity and temperature via the solution of a Landau amplitude equation. The latter are being used in evaluating the Nusselt number representing the average heat transfer coefficient in dimensionless form. No oscillatory convection is possible when the Coriolis effect is small and negligible.