| Summary: | Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution April 1992 A pair of simple models representing the interaction of a continuously stratified f-plane quasigeostrophic lens with a uniform external shear flow is examined. The study is motivated by the desire to understand the processes that affect Mediterranean Salt Lenses and other mesoscale lenses in the ocean. The first model represents the eddy as a pair of quasigeostrophic 'point potential vortices' in uniform external shear, where the two point vortices are imagined to represent the top and bottom of a baroclinic eddy. While highly idealized, the model succeeds in qualitatively reproducing many aspects of the behavior of more complex models. In the second model the eddy is represented by an isolated three dimensional patch characterized by quasigeostrophic potential vorticity linear in z, in a background flow with constant potential vorticity. The boundary of the lens may be deformed by interactions with a uniform background shear. A family of linearized analytical solutions representing such a vortex is discussed in Chapter 3. These solutions represent lens-like eddies with trapped fluid cores, which may propagate through the surrounding water when there is external vertical shear. The analysis predicts the possible forms of the boundary deformation in a specified external flow, and the precession rate of normal mode boundary perturbations in the absence of external flow. The translation speed of the lens with respect to the surrounding fluid is found to be a simple function of the external vertical shear and the core baroclinicity. A numerical algorithm which is a generalization of the contour dynamics technique to stratified quasigeostrophic flow is used to extend the linear results into the nonlinear regime. This numerical analysis allows a determination of the range of environmental conditions (e.g., the maximum shear ...
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