Contents

• Contents
• List of Figures
• List of Tables
• Introduction
• Presentation of the Numerical Methods
  • The Time Discretization
  • Finite Difference Models
    • Introduction
    • The Three Staggerings Used
  • Finite Element Models
    • Introduction
    • The Galerkin Formulation
    • The Different Finite Element Models Tested
  • The Discontinuous Spectral Element Method
    • Introduction
    • The Model Formulation
    • Adaptive Mesh Refinement
    • Curved Spectral Element Method
  • Summary
• Testing the Different Numerical Methods
  • Gravity Waves in a Square Domain
  • The Wind-driven Circulation in a Circular Domain
  • Conservative Properties of the Different Numerical Formulations for a Nonlinear Problem
  • The Munk Problem in a Square Domain
  • Conclusions
• Finite Difference Methods in Rotated Basins
  • Introduction
  • Vorticity Budgets in a C-grid SW Model
    • The General Form of the Discretized Vorticity Budget
    • Numerical Formulations
    • Results
  • Vorticity Budgets in SW B-grid Models
  • The Quasi-Geostrophic Model
    • Discretization
    • Results
  • Discussion and Conclusion
• Single Gyre Circulation in Irregular Domains
  • Review of the Single Gyre Problem with Free-Slip Boundary Conditions
  • Model Selection and Experimental Design
  • Results
    • General Results for all Geometries
    • Role of the Transients for Geometry V at High Reynolds Number
  • Scale Analysis and Discussion
  • Adaptivity
  • Conclusions
• Conclusions
• an A-grid energy conserving formulation
• Model vorticity budget on a B-grid
• Bibliography

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