DYNAMICAL STRUCTURE OF COMPRESSIBLE-FLUID FLOWS IN AN ABRUPTLY ROTATING CYLINDER

Abstract

Time-dependent motions of a compressible fluid in response to an abrupt rotation of the cylindrical container are considered. Concern is directed to the case of a rapidly-rotating cylinder; the reference Ekman number, E, is very small and the peripheral Mach number M almost-equal-to O(1). Numerical solutions to the complete Navier-Stokes equations are secured to appraise the relative importance of the major dynamical ingredients in the flow process. These endeavors are complementary to earlier works which demonstrated the global evolution of the dominant velocity component. The magnitudes of the terms of the azimuthal momentum equation are evaluated to enable specific comparisons of the dynamics effects involved. At high Mach numbers, the oscillatory behavior of the main flow is shown to be attributable to thermo-acoustic modes. The radial density stratification is strengthened as the Mach number increases; because of this, the fluid in larger portions of the cylinder interior experiences rarefaction and cooling. The consequence turns up in the form of retardation of the overall spin-up process as M increases.