ON THE 3-DIMENSIONAL INSTABILITIES OF PLANE FLOWS SUBJECTED TO CORIOLIS-FORCE

Linear stability of two-dimensional flows in a frame rotating with ang ular velocity vector Omega=Omega e(z) perpendicular to their plane is considered. Sufficient conditions for instability have been derived fo r simple inviscid flows, namely parallel shear flows (characterized by the ''Pedley'' or ''Bradshaw-Richardson'' number), circular vortices (by the ''generalized Rayleigh'' discriminant) and unbounded flows hav ing a quadratic streamfunction (with elliptical, rectilinear or hyperb olic streamlines). These exact criteria are reviewed and contrasted us ing stability analysis for both three-dimensional disturbances and ove rsimplified ''pressureless'' versions of the linear theory. These sugg est that one defines a general inviscid criterion for rotation and cur vature, based on the sign of the second invariant of the ''inertial te nsor,'' and stating that, in a Cartesian coordinate frame: a sufficien t condition for instability is that Phi(x,y)=-1/2S:S+1/4W(t).W-t<0 som ewhere in the flow domain. It involves the ''tilting vorticity'' W-t=W +4 Ohm[Cambon et al., J. Fluid Mech. 278, 175 (1994)] and the symmetri c part S of the velocity gradient of the basic flow. (C) 1997 American Institute of Physics.