LINEAR-STABILITY OF COMPRESSIBLE TAYLOR-COUETTE FLOW

A temporal stability analysis of compressible Taylor-Couette flow is presented. The viscous flow studied in this paper is contained between two concentric cylinders of infinite length, which are rotating with different angular velocities and are kept at different surface temperatures. The linear stability analysis based on the Chebyshev collocation spectral method can be used to determine both the mode of the disturbance to be first excited and the corresponding eigenfunctions. The effects of differential rotation and temperature difference on the stability of Taylor-Couette flow are contrasted for a range of Mach numbers ranging from incompressible to Mach 3.0. The relative motion of the cylinders dramatically affects the characteristics of the Couette flow at the onset of instability. It is found that, at subsonic speeds of the inner cylinder, the only unstable mode is the axisymmetric first mode. However, more than one unstable mode appear at supersonic cylinder speeds, with the dominant one remaining the first mode. The flow is stabilized or destabilized depending upon the temperature ratio and speeds of the two cylinders. Independent of Mach number and temperature ratio, increasing Reynolds number generally promotes a destabilizing effect, indicating its inviscid nature of the Taylor-Couette flow.