The Finite Element Ocean Model and its aspect of vertical discretization

The ocean bottom topography influences the general ocean circulation through a variety of processes. They can be of dynamical origin like topographic Rossby waves and topographic steering of the circulation through the bottom pressure torque, or of geometrical origin like sills and ridges that determine the pathways and properties of water masses. A faithful representation of the bottom topography and relevant physical processes is required in numerical ocean models. The ability of a model to resolve the bottom topography is mainly determined by the choice of vertical coordinates or vertical grids, which is one of the most important aspects of the model design.This work is focused on a systematic study of the performance of different vertical grids in a set of numerical experiments performed with the Finite Element Ocean circulation Model (FEOM). This model supports several types of vertical discretization within a single numerical core, which allows the effects of vertical discretization to be isolated from other numerical issues.A new version of FEOM is developed during the course of this work. Its discretization is based on unstructured triangular meshes on the surface and prismatic elements in the volume. The model uses continuous linear representation for the horizontal velocity, surface elevation, temperature and salinity, and solves the standard set of hydrostatic primitive equations. The characteristic-based split (CBS) scheme is used to suppress computational pressure modes and to stabilize momentum advection. With this split method the cost of solving the dynamic equations is reduced by uncoupling velocity from surface elevation. An algorithmfor calculating pressure gradient forces is introduced to reduce pressure gradient errors on sigma or hybrid grids. Different advection schemes are implemented and tested for tracer equations. The model as a whole is built with the hope of providing an efficient and versatile numerical tool for ocean sciences. It is capable of representing boundaries faithfully and allows flexible local mesh refinement without nesting. The grids explored in this work include: the full cell z-level grid, the sigma grid, the combined z sigma grid and the modified z grids with partly or fully shaved bottom cells. Three numerical experiments are carried out to illustrate the performance of these types of grids. The first one deals with a steadily forced flow past an isolated seamount, the second one simulates topographic waves over sloping bottom in a rotating stratified channel, while the third one studies the dense water overflows in an idealized configuration. It is shown that representing the bottom with shaved cell grids improves representation of ocean dynamics significantly compared to the full cell case. However, the sigma and z sigma grids are still better suited for representing bottom intensified currents and bottom boundary layer physics, as they can provide necessary vertical resolution in addition to continuous bottom representation. Taking into account the issue of pressure gradient errors, z sigma grids are the promising approach for realistic simulations.Intercomparison of our results with those published in theliterature validates the performance of FEOM. With the development effort through the current work, FEOM has become a versatile tool for general oceanographic applications.