Axisymmetric convection between two rotating disks

Abstract

A real fluid is contained between two horizontal infinite disks which rotate about a common vertical axis with the same angular velocity. On the upper disk there is an axisymmetric non-uniform temperature distribution with a minimum at the point of intersection of the disk and the axis of rotation. The lower disk is insulated. It is assumed that inertial accelerations are negligible in comparison with Coriolis accelerations and that viscous effects are confined to Ekman layers at the disks. Outside the Ekman layers, therefore, since the motion is axisymmetric, the buoyancy forces, by the geostrophic approximation, drive only an azimuthal component of the velocity field which cannot alter the temperature field. Thus heat is convected only by the secondary circulation which is driven by the viscous forces of the Ekman layers. It is possible then for the secondary flow to be so small that heat is transferred by conduction processes.This paper analyses the conditions necessary for either conduction or convection processes to predominate and the structure of the velocity and temperature fields in these different situations. In addition the separate effects of a temperature maximum on the upper disk and of replacing the upper disk by a stress-free surface are considered.