Shear flow instabilities in a rotating system

Abstract

The stability of a plane parallel shear flow with the profile U(z) = tanh z is considered in a rotating system with the axis of rotation in the z-direction. The establishment of the basic flow requires a baroclinic state, but baroclinic effects are suppressed in the stability analysis by assuming a limit of high thermal conductivity. It is shown that the strongest growing disturbance changes from a purely transverse form in the limit of vanishing rotation rate to a nearly longitudinal form as the angular velocity of rotation increases. An analytical solution of the stability equation is obtained for vanishing growth rates of the transverse form of the instability. But, in general, the solution of the problem requires numerical integrations which demonstrate that the preferred direction of the wave vector of the instability is towards the left of the direction of the mean flow.