Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
NUMERICAL MODELING OF WAVE-INDUCED CURRENTS USING A PARABOLIC
WAVE EQUATION
By
HARLEY STANFORD WINER
August 1988
Chairman: Dr. Hsiang Wang
Major Department: Aerospace Engineering, Mechanics and Engineering Science
Prediction of waves and currents in the nearshore region in the presence of proposed
breakwaters is needed in the design process in order to optimize the placement of the
structures. A numerical model is developed which solves for the wave field, the depth
averaged mean currents and the mean water surface elevation within a given computa
tional domain with the presence of breakwaters. The model iterates between a wave model
and a circulation model. The wave model uses a parabolic approximation to a combined
refraction-diffraction mild slope equation which includes currents. The circulation model
uses an alternating direction implicit method solution to the depth averaged equations of
momentum using the radiation stress terms obtained through solution of the wave model as
the forcing terms. Each of the terms in the depth averaged equations of momentum involve
assumptions that are discussed in the report. The model is constructed in modular form so
that improvements can easily be incorporated into the model.
The model was employed for several test cases such as rip channels, bar gaps, and
both shore perpendicular and shore parallel breakwaters. Good agreement was obtained
when the model was used to simulate a laboratory experiment of Michael R. Gourlay
(Wave set-up and wave generated currents in the lee of a breakwater or headland,
Proc. 14*^ Coastal Eng. Conf., Copenhagen, 1974, pp. 1976-1995).
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