Date of Award

Spring 1-1-2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Mathematics

First Advisor

Thomas Manteuffel

Second Advisor

Steve McCormick

Third Advisor

John Ruge

Fourth Advisor

Frank Bryan

Fifth Advisor

Marian Brezina

Abstract

An alternative First Order Least-Squares (FOSLS) Finite Element formulation for the numerical solution of the stationary linear problem posed by the Beta-Plane approximation of wind driven ocean circulation is presented. The equations of interest are incompressible Navier-Stokes in a rotational frame of reference. The formulation is considered in all three spatial dimensions, i.e., without the hydrostatic hypothesis most often used in other numerical models based on the hydrostatic primitive equations. In order to validate the computer model, a classical experiment for Beta-Plane approximation of wind driven ocean circulation is utilized. To this extent, the sliced cylinder model introduced by Pedlosky & Greenspan (1967) defines the physical domain. The focus of the validation process is the analysis of the solution for two expected phenomena, the thin Ekman layers induced in the system as well as the east-west asymmetry of the pressure field for the interior circulation.

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