# Zhigang Xu

## Thesis Approved May 1995

*
Wave- and Wind-Driven Flow on the Continental Shelf*
An Eulerian description of mean wave forcing, under the effects of the
Earth's rotation and fluid friction, is derived. A general set of
equations for the mean flow that includes wave forces is established, and a
linearized system is extracted for further study. The study of the
linearized system focuses on the response of an Eulerian water column to
wave forces, including a step function forcing and arbitrary forcing. The
response to steady wave forcing yields a formula for wave-driven flow
which unifies the early work of Longuet-Higgins (1957), Hasselmann (1970),
and Madsen (1978). Generalization of the results obtained with
monochromatic waves to random waves is briefly discussed. Implication of
the wave-driven flow to classical shelf dynamics is discussed with an
example. A pre-existing CASP data set was explored to test the theory of
wave driven flow. The results from this preliminary exploration emphasize
the need for an experiment specially designed for investigating flows
driven by Coriolis-induced wave stress.

The second part of the thesis introduces a new method for the numerical
modelling of the linearized three-dimensional equations for shelf circulation.
The method makes full use of the local water column response to Heaviside
step force in modelling the global response to arbitrary external forcing
in a three-dimensional domain. It is shown that the method can save
substantial computational time. This can be valuable in a problem involving
repeated integration of the equations of motion, such as data assimilation.
An optimum velocity splitting form is also provided for accelerating the
convergence of the calculation. Also discussed is the advantage of the
*eta - Q* grid, which is introduced during the development of the method.