|Date:||Thu, February 10, 2011|
|Place:||Campus Center, IRC (East Wing) Seminar Room|
Abstract: We derive a family of models for shallow water near geostrophy via asymptotic expansion of the shallow water Lagrangian in Rossby number. The models allow for spacial variations in Coriolis parameter and bottom topography and possess conservation laws for energy and potential vorticity. We study the family on double periodic domain proving global well-posedness for certain values of parameters. Due to topological reasons rotating shallow water models in periodic setting can be derived as Euler-Poincare equations only for zero-mean Coriolis parameters. We show that this restriction disappears on the Hamiltonian side of variational principle for a large class of affine Lagrangians and, in particular, for the family we derive. In doing so we expose the equations as Hamiltonian on an appropriate diffeomorphism group with respect to a non-canonical symplectic form.