A corrector for the sverdrup solution for a domain with islands

Abstract

In this paper we look at the influence of the Coriolis force on the quasi-geostrophic equations on a domain with islands. We prove that asymptotically we obtain the solution of the Sverdrup equation with homogeneous Dirichlet conditions on the inward boundary plus a corrector function which takes into account the presence of the islands. This work is motivated by the fact that in oceanography most of the surfaces are not simply connected. This is the case for example for the North Pacific with the Japanese islands. At our knowledge, in all the previous mathematical works, just simply connected domains have been considered. Finally we will give some simple numerical simulations related to the Stommel model to see the importance of the corrector.

Keywords:

• Ocean circulation
• Asymptotic model
• Singular perturbations
• Islands
• AMS Subject Classification: 35Q30
• 35B40
• 76D05

Acknowledgments

The first author would like to thank Professor Alain Colin de verdière for interesting discussions on this paper. After the redaction of this paper, he indicates him the physical paper written by J. Pedlosky et al. The second and third authors have been partially supported by the C.I.C.Y.T. project MAR98–0486.

Notes

^†E-mail: [email protected], [email protected]

Additional information

Notes on contributors

M.A. Rodríguez-Bellido

†E-mail: [email protected], [email protected]