A family of Hamiltonian balanced models for rotating shallow water near geostrophy
- When?
- Friday 30 April 2010, 16:00 to 17:00
- Where?
- 24AA04
- Open to:
- Students, Staff
- Speaker:
- Dr. Sergiy Vasylkevych (Jacobs University, Bremen)
Abstract: We derive a new family of models for shallow water near geostrophy via asymptotic expansion of the shallow water Lagrangian in Rossby number and study this family on a periodic domain.
Due to topological reasons rotating shallow water models in periodic setting can be derived as Euler-Lagrange 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. Using particle relabeling symmetry one is able to reduce the phase space to an affine hyperplane in the space of fluid height distributions. Finally, we show the well-posedness of the models for all but one value of the free parameter.
