Poisson geometry and first integrals of geostrophic equations
Differential Geometry
2009-11-13 v1 Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.0802.4439,
title = {Poisson geometry and first integrals of geostrophic equations},
author = {Boris Khesin and Paul Lee},
journal= {arXiv preprint arXiv:0802.4439},
year = {2009}
}
Comments
6 pages, to appear in Physica D