Comparison of numerical methods for modelling ocean circulation in basins with irregular coasts

摘要: Comprehension of global oceanic currents and, ultimately, of climate variability requires the use of computer modelling. Although much effort has been spent on the aceuracy of traditional finite difference (FD) models used in ocean modelling, there are still eoncerns, especially siDce these models have a crude representation of the geometry of oceanic basins. Such a erude representation may influence the accuracy of modelling boundary eurrents, or ùnrealisticly represent the impinging of eddies or the propagation of Kelvin waves along the coastline. This motivated the use of alternative modelling techniques applied on completely irregular geometries such as finite element (FE) and spectral element (SE) methods. In this thesis. we want to investigate the aceuracy and cost-effectiveness of these three numerical methods in irregular domains and to understand to which extent the unstructured grid FE and SE methods constitute an improvement over the more traditional FD methods. To accomplish this, we limit ourselves to modelling the shallow water equations in presence of irregular coastlines with no bottom topography.In the first part of the thesis, we compare the performances of FD methods on Cartesian grids\Vith FE and SE methods in various geometries for linear and nonlinear applications. vVe argue that the SE method is to a certain extent superior to FD methods. In a second part, we study the influence of step-like walls on vorticity budgets for wind-driven shallow water FD models. vVe show that vorticity budgets can be very sensitive to the FD formulation. This has certain implications for using vorticity budgets as a diagnostic tool in FD …