A semi-Lagrangian finite element barotropic ocean model /

The purpose of this thesis is to develop a new barotropic ocean model to study ocean dynamics. The model combines for the first time the flexible finite-element method and an accurate semi-Lagrangian advection scheme on unstructured triangular meshes.In the first part of the work, the semi-Lagrangian method is used for advection experiments on an irregular grid. A cosine hill is advected using a specified flow field corresponding to solid body rotation. A major difficulty is to find an interpolator which is at least fourth order accurate on an unstructured mesh. Such accuracy is needed for the treatment of slow Rossby waves in ocean models. We develop such a method using a kriging interpolating scheme. The results are better than fourth order accurate on an unstructured grid. Such accuracy is achieved at a reasonable computational cost due to the increased flexibility of unstructured meshes and accuracy of the kriging approach.The second part of the thesis examines the finite-element spatial discretization of the linear inviscid shallow-water equations with a semi-implicit temporal discretization on unstructured meshes. The finite-element velocity-pressure pair should ideally give noise-free results when solving geostrophic balance, and fulfill at the same time certain consistency conditions. We show most of the known finite-element pairs do not satisfy these two requirements simultaneously, except for an unconventional and unnamed low-order element pair. The latter gives good results for experiments on the propagation of gravity waves using the linear inviscid shallow-water equations.The last part of the thesis examines the coupling between semi-Lagrangian advection and semi-implicit treatment of the linear gravity wave terms on unstructured meshes. We use kriging as interpolator for semi-Lagrangian advection and the unconventional finite-element pair previously examined for the nonlinear shallow-water equations. The propagation of a typical oceanic eddy is simulated without forcing