Date of Award

Spring 1998

Document Type


Degree Name

Doctor of Philosophy (PhD)


Ocean & Earth Sciences

Committee Director

A. D. Kirwan, Jr.

Committee Director

C. E. Grosch

Committee Member

J. A. Adam

Committee Member

T. B. Gatski

Committee Member

D. G. Lasseigne


A particle-in-cell (PIC) model is developed and applied to problems involving the evolution of warm-core rings. Such models are a hybrid of conventional Eulerian and Lagrangian models. They are ideally suited for problems in which a lower layer outcrops to the surface, such as at the boundary of a ring.

The model is developed in three implementations. First, for purposes of model validation, a reduced gravity model is described. The PIC model reproduces the essential characteristics of analytical solutions to the reduced gravity equations and integral invariants are conserved to a high degree. Next, a 1.5-layer model is developed and used to study the effects of environmental forcing on the evolution of warm-core rings. This model incorporates forcing by a prescribed velocity field in the lower layer. Three solution regimes are found by varying components of the forcing. In the first regime, the eddy becomes elliptical and rotates anticyclonically. For solutions in this regime, a relationship between the forcing magnitude and ring rotation rate and ellipticity is obtained. In the second regime, the eddy becomes highly elliptical, sheds satellite vortices and then rotates as in the first regime. This regime has not been reported previously. In the third regime the eddy is stretched into an elongated filament and never reforms into a coherent vortex. The boundaries between these regimes are defined as a function of the forcing velocity components. Finally, the two-layer model is described. This model solves the primitive equations for a two-layer, shallow-water ocean. Thus, no assumptions or restrictions on the flow in either layer need be made. In order to test this model, three new analytical steady-state solutions to the shallow-water equations are derived. Model results compare favorably to the analytical solutions.

A parallel algorithm for the PIC technique is given. All models were implemented on a parallel processing computer using Message Passing Interface. The parallel implementation of the models virtually eliminates restrictions on resolution, and timings show nearly a one-to-one speed-up with the number of processors with up to 16 processors.


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