Abstract
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 → ∞. The construction is based on the known correspondence SU( N) → SDiff( T 2) when N → ∞ between the finite-dimensional group of unitary unimodular N × 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. 7
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