Energy transfer in the transient Ekman layer of a compressible fluid

Abstract

A theoretical analysis is made of the transient Ekman layer of a rapidly rotating compressible fluid. In the initial state, both the fluid and the disk are in equilibrium in isothermal rigid-body rotation. Flow is initiated by imposing a mechanical/thermal disturbance on the rotating disk. By making detailed examinations of the energy balance in the Ekman layer, the energy transfer mechanisms are delineated. Two distinctive transient energy transfer mechanisms are identified: (i) the one-dimensional energy diffusion process in the axial direction, and (ii) the conventional Ekman layer flow which is similar to that of an incompressible fluid. The usefulness of a particular grouping of flow variables, which is termed the energy flux content, is emphasized. The major distinctions between compressible and incompressible fluids are ascertained. This analytical endeavour clarifies the features unique to a compressible rotating flow. A unified view is constructed to encompass the previously published theoretical findings which had been presented in a piecemeal fashion.