Stability of stagnation points in rotating flows

The Lifschitz and Hameiri theory for short-wave instabilities is used to show that any steady inviscid plane flow subjected (or not) to a Coriolis with perpendicular angular velocity vector is unstable to three-dimensional perturbations if Phi(x(0)) < 0 on a stagnation point located at x(0). Phi is the second invariant of the inertial tensor [Leblanc and Cambon, Phys. Fluids 9, 1307 (1997)]. The particular cases of zero absolute W(x(0)) + 2 Omega = 0 and zero tilting W(x(0)) + 4 Omega = 0 vorticities are also considered. The criterion is applied to Chaplygin's non-symmetric dipolar vortex moving along a circular path, which is shown to be unstable. (C) 1997 American Institute of Physics.