The Second Stability Boundary for Circular Couette Flow

Abstract

To investigate the stability of an axisymmetric vortex flow between rotating cylinders, the development of non-axisymmetric small disturbance is analyzed by a systematic expansion procedure in the amplitude of the vortex. The amplification rate of the disturbance is determined as a power series in the amplitude. The series is truncated with the fourth order in the numerical calculation. It is found that the disturbance grows most rapidly when its axial wave number coincides with that of the vortex. The second boundary representing the stability criterion of the vortex flow is calculated for a small gap of the cylinders. When the ratio of angular velocities is specified, the critical value of axial wave number for the vortex flow is found to be smaller than the critical wave number given by the classical stability problem.