Poisson geometry and first integrals of geostrophic equations

PHYSICA D-NONLINEAR PHENOMENA

卷:237

Article

Khesin, Boris¹  Lee, Paul¹ 

[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

关键词: geostrophic equations;    enstrophy invariants;    Poisson structure;    wasserstein space;    Hamiltonian reduction;    diffeomorphism group;   

DOI  :  10.1016/j.physd.2008.03.001

来源: Elsevier

【 摘 要 】

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. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free