Poisson geometry and first integrals of geostrophic equations

Details Poisson geometry and first integrals of geostrophic equations Poisson geometry and first integrals of geostrophic equations

2008-02-29

arxiv.org/abs/0802.4439v1

Mathematics

Differential Geometry

6 pages, to appear in Physica D

Scientific paper

10.1016/j.physd.2008.03.001

We describe first integrals of geostrophic equations, which are similar to the enstrophy invariants of the Euler equation for an ideal incompressible fluid. We explain the geometry behind this similarity, give several equivalent definitions of the Poisson structure on the space of smooth densities on a symplectic manifold, and show how it can be obtained via the Hamiltonian reduction from a symplectic structure on the diffeomorphism group.

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