| Abstract: |
| When the length scale of the flow is on the same order as
the Rossby deformation radius, which is often the case in the interior
of the flow, the classical rigid-lid assumption is
no longer valid, the impact of the free surface/interface deformations
on the
the vorticity field is no longer negligible, and therefore it has to
be accounted for in the model. In this talk, we present some
new results concerning the well-posedness of the barotropic
quasi-geostrophic equation and the multi-layer QG equations, where the
top surface, and the layer interfaces for the multilayer QG, are left
free to evolve. It will be shown
that, when the free surface/interfaces are included as components of the
potential vorticity, the models remain globally well-posed, under
certain generic assumptions on
the initial state and the boundary of the domain. |
|