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Development of a Simplified Adaptive Finite Element Model of the Gulf Stream

The goal of this dissertation is to look at the feasibility of incorporating a moving adaptive mesh refinement procedure into an existing finite element model of the shallow water equations. The Stommel model simulates simple oceanic flows including western boundary currents like the Gulf Stream. This dissertation describes the finite element formulation of the Stommel equations, a modified form of the shallow water equations. The feasibility of including a mesh movement procedure based on monitor functions is looked at, with a study of one particular monitor. Results are shown for a specific mesh velocity and for mesh velocities computed from this monitor. We conclude that the monitor function used is a promising start at finding a way to allow the mesh to dynamically evolve with the flow, in applications such as this.