An asymptotic analysis of the Taylor-Proudman flow in a rapidly-rotating compressible fluid

압축성 회전유체에서 발생하는 Taylor-Proudman 유동에 대한 점근해석

A matched asymptotic analysis is conducted for a 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 Park & Hyun, 2002) by means of the energy balancing analysis, have been re-derived. The concept of the variable, the energy content $e[{\equiv}T+2 {\alpha}^2 {\gamma}{\nu}]$, 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, numerous admissible theoretical solutions for interior flow exist with an associated wail boundary condition. Some canonical examples are illustrated with comprehensive physical descriptions. The differential heating problem on the top and bottom endwall disks is revisited by using the concept of the energy content. The results are shown to be in line with the previous findings.