HAMILTONIAN FINITE-DIMENSIONAL MODELS OF BAROCLINIC INSTABILITY

A hierarchy of N-dimensional systems is constructed starting from the standard continuous two-layer quasi-geostrophic model of the geophysic al fluid dynamics. These models (''truncations'') preserve the Hamilto nian structure of the parent model and tend to it in the limit N --> i nfinity. The construction is based on the known correspondence SU(N) - -> SDiff(T-2) when N --> infinity between the finite-dimensional group of unitary unimodular N x N matrices and the group of symplectic diff eomorphisms of the torus and the fact that the above-mentioned continu ous model has an intrinsic geometric structure related to SDiff(T-2) i n the case of periodic boundary conditions. A fast symplectic solver f or these truncations is proposed and used to study the baroclinic inst ability. (C) 1997 Published by Elsevier Science B.V.