The Taylor-Proudman column in a rapidly-rotating compressible fluid II. asymptotic analysis

Abstract

A matched asymptotic analysis is conducted for compressible rotating flow in a cylindrical container when a mechanical and/or a thermal disturbance is imposed on the wall. The system Ekman number is assumed to be very small. The conditions for the Taylor-Proudman column in the interior, which were also given in the companion paper (Ref. [1]) for energy transports by means of the energy balancing analysis, have been re-derived. The concept of the grouping of variables, the energy flux content e ≡ T + 2α2rv, is reformulated, and its effectiveness in characterizing the energy transport mechanism is delineated. It is seen that, under the condition of the Taylor-Proudman column, there exist numerous admissible theoretical solutions for interior flow pertinent to the imposed wall boundary condition. Some canonical examples are illustrated. The differential heating problem on the top and bottom endwall disks is revisited by using the concept of the energy flux content. The results are shown to be in line with the previous findings.