HAMILTONIAN FINITE-DIMENSIONAL MODELS OF BAROCLINIC INSTABILITY

摘要

A hierarchy of N-dimensional systems is constructed starting from the standard continuous two-layer quasi-geostrophic model of the geophysical fluid dynamics. These models (''truncations'') preserve the Hamiltonian structure of the parent model and tend to it in the limit N --> infinity. 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 diffeomorphisms of the torus and the fact that the above-mentioned continuous model has an intrinsic geometric structure related to SDiff(T-2) in the case of periodic boundary conditions. A fast symplectic solver for these truncations is proposed and used to study the baroclinic instability. (C) 1997 Published by Elsevier Science B.V. [References: 18]