List of Tables

• List of variables in (2.1-2.2)
• Refinements parameters used in the simulations unless otherwise specified.
• Convergence order for the different models for the linear wave experiment in a square domain. For all models, the order is fairly close to their theoretical value. Models using unstructured grids lost almost an order for the error in v compared to the error in u.
• Convergence order in elevation, for the different models for the linear wind-driven experiment in a circular domain without Coriolis terms.
• Convergence order for the different models for the nonlinear Munk problem in a square domain.
• The four combinations of advection formulations and stress tensor formulations.
• Summary of the vorticity budget and kinetic energy diagnostics for the B-grid after a spin-up of 6 years.
• Notations for the finite volume method

ACKNOWLEDGEMENTS

Many thanks go to my supervisors, Charles Lin and David Straub, for their support and the proof-reading of the thesis. David Straub is in particular acknowledged for his important contribution to Chapters 4 and 5.

The C2GRC group at McGill was a great place for meeting and listening to world-renowned scientists. I must thank in particular Lawrence Mysak for inviting me along on numerous occasions for after-seminar beers or suppers. Many McGill PhD students left the department in the course of my studies and I am indebted to them for engrossing scientific conversations we had around a few beers. Thanks therefore go to Rob Scott, Halldor Bjornsson, Martin Charon, Daniel Le Roux, Bruno Tremblay, Daniel Bourgault, Stephen Newbigging and three cornerstones of the department, Rick Danielson, Werner Wintels and Marco Carrera.

Deep thanks go to Catherine Mavriplis for discussion about error-estimators in adaptive spectral element methods and Julien Dompierre for the remeshing strategies. Stephen Newbigging, Ted Tedford, Drew Peterson and Jason Chaffey corrected the spelling and the English grammar. CERCA (Centre de recherche en calcul appliqué) provided me with an excellent working environment. Many thanks go to the CERCA staff, scientists and other PhD students in general for their support and discussions.

I must also thank my father for motivating me to do a PhD in North-America despite the great distance and stretched family bounds implied by doing so.

This research was supported by NSERC and CCGCR. VU (developed at CERCA) GMT, Gnuplot and Ferret are the graphical packages used in this thesis.