Instability of rigidly rotating flows to non-axisymmetric disturbances

An investigation of the hydrodynamic stability of swirling flows having arbitrary Rossby numbers is described. A necessary condition for instability is derived for rigidly rotating flows and this condition is further refined in the specific case of a parabolic axial flow. Numerical results are presented for two azimuthal wave-numbers corresponding to the maximum growth rates of unstable perturbations as a function of Rossby number. It is found that the largest growth rates occur when the Rossby number is O (1) and that instability persists for surprisingly large values of this parameter. Previous explanations of the instability mechanism are discussed and it is concluded that these are only adequate in the limit of small Rossby number.