EFFECTS OF THE CORIOLIS-FORCE ON THE STABILITY OF STUART VORTICES

A detailed investigation of the effects of the Coriolis force on the t hree-dimensional linear instabilities of Stuart vortices is proposed. This exact inviscid solution describes an array of co-rotating vortice s embedded in a shear flow. When the axis of rotation is perpendicular to the plane of the basic flow, the stability analysis consists of an eigenvalue problem for non-parallel versions of the coupled Orr-Somme rfeld and Squire equations, which is solved numerically by a spectral method. The Coriolis force acts on instabilities as a 'tuner', when co mpared to the non-rotating case. A weak anticyclonic rotation is desta bilizing: three-dimensional Floquet modes are promoted, and at large s panwise wavenumber their behaviour is predicted by a 'pressureless' an alysis. This latter analysis, which has been extensively discussed for simple flows in a recent paper (Leblanc & Cambon 1997) is shown to be relevant to the present study. The basic mechanism of short-wave brea kdown is a competition between instabilities generated by the elliptic al cores of the vortices and by the hyperbolic stagnation points in th e braids, in accordance with predictions from the 'geometrical optics' stability theory. On the other hand, cyclonic or stronger anticycloni c rotation kills three-dimensional instabilities by a cut-off in the s panwise wavenumber. Under rapid rotation, the Stuart vortices are stab ilized, whereas inertial waves propagate.