Date of Award
Doctor of Philosophy (PhD)
A. D. Kirwan, Jr.
Larry P. Atkinson
A model of lens-shaped anticyclonic eddies based on nonlinear shallow water equations is developed. The model is a three-layer fluid and allows for one asymmetric mode as well as specified environmental flows. The solution scheme is a polynomial expansion of the field variables. When inserted into the hydrographic equations, the expansion yields eight first-order differential equations for the time dependent amplitudes. This system of ordinary differential equations is numerically tractable. As long as the initial values meet the requirement of elliptical structure and the prescribed external force is tolerable for the initial values, the numerical solutions are stable. Numerical solutions are developed which show a wide variety of characteristics. Using different assumptions, six analytical solutions are obtained and discussed. For isolated lenses, three special solutions show different oscillations of the amplitudes. One has only the inertial frequency. The other two have superinertial and subinertial frequencies, respectively. For forced lenses, three special solutions are related to different exterior prescribed flows. One is an equilibrium solution having a steady-state external flow. The two other solutions are derived from external flows with subinertial and inertial frequencies, respectively. An attempt is made to apply the special solutions to observations of warm-core eddies in the Gulf of Mexico and other regions of the world ocean. The simulations of warm-core eddies with the special solutions are in general agreement with available data.
"Some Solutions to a Lens Model With Applications to Warm-Core Eddies"
(1992). Doctor of Philosophy (PhD), dissertation, Ocean/Earth/Atmos Sciences, Old Dominion University, DOI: 10.25777/rv1m-kx91