Spectral analysis of asymmetric disturbed Couette flow and related problems of hydrodynamic stability (Q1907408)

We consider the flow of an ideal incompressible fluid between two rotating cylinders. Based on studies of exponentially time-dependent disturbances, we reduce the motion stability problem to the problem of localizing the spectrum of the corresponding spectral problem. The Rayleigh relation yields a necessary and sufficient condition under which the flow of a fluid is stable relative to rotationally symmetric disturbances. By considering asymmetric disturbances, we are led to a broader essential spectrum. Therefore, to solve the stability problem for the flow of a fluid it is necessary to describe the fluid and to localize the discrete spectrum.