Stability of flow in a rotating viscous incompressible fluid subjected to differential heating

Abstract

An attempt is made to find a theoretical explanation for the type of flow observed when a liquid is subjected at the same time to rotation and to a horizontal temperature gradient. W hen the liquid is contained between two concentric cylinders it is known from experiment that two distinct types of flow occur, one in which the motion is in the form of a meridional vortex with the addition of a zonal component, and the other in which the motion exhibits a meandering wave-like pattern. Of vital importance as regards the type of flow is found to be a parameter defined as the Rossby number for the problem, and two sets of critical values of this parameter are found which bound the range over which wave motion is possible. Qualitatively this is in complete agreement with experimental observations, but quantitative results show some discrepancy between theory and experiment.