Analogous behavior of rotating and stratified fluids

Abstract

The prsent paper continues an investigation on the analogy between fluids which are rotating and fluids which are stratified. The analysis has been extended to include rotation in the stratified system and stratification in the rotating system. Even though the basic equations are the same we differentiate between the two systems on the basis of the forces which drive the motion. System SΩ corresponds to adding rotation to the stratified system S, in a foregoing paper where the flow is driven by differential heating at the side boundaries. In system Ω_S stratification is added to the rotating fluid, Ω, which is driven by differential vertical vorticity at the top and bottom boundaries. It is shown that an exact analogy continues to hold when the flow is two-dimensional and when certain variables are identified with each other in the two systems. Combining rotation and stratification of the same order inhibits the outflow from the boundary layers which was found to be necessary in the simple systems, and the buoyancy and Ekman boundary layers play no role in two-dimensional flow. The entire fluid is dominated by diffusive processes. In system SΩ three-dimensional flows have significant buoyancy layers. When the added process (rotation in system SΩ or stratification in system Ω_s) is introduced as a higher-order correction, it can lead to zero-order changes in two-dimensional flows but has only higher-order effects in the three-dimensional SΩ system. It is also shown that the rotating, stratified fluid has no boundary layers of the type found by Stewartson (1957) for rotating homogeneous fluids.