ON THE DIFFERENTIAL GEOMETRY APPROACH TO GEOPHYSICAL FLOWS

It is shown that a variety of geophysically relevant flows admit a geo metric interpretation and may be treated as geodesic flows on certain infinite-dimensional manifolds. As an illustration of this approach we present an example of the quasi-geostrophic flows. The curvature tens or determining the separation of geodesics and, hence, stability is ca lculated. It is shown that on the f-plane the curvature in the section s containing a stationary periodic flow with a stream function given b y cos(kx+ly) and a perturbation of the same functional form is negativ e, like in the case of conventional 2-d hydrodynamics. On the contrary , for any stationary shear flow on the beta-plane the curvature is alw ays positive for large enough values of beta.