104
particular the comparison to the laboratory experiments of Gourlay) confirm the predictive
capability of the numerical model. The simplifications mentioned above make this possi
ble, for there must be a mathematical statement of the physical process before numerical
modelling of the process can even be attempted.
In making recommendations for further study we should distinguish between short range
objectives and the possibilities that may become open to numerical modelers by advances
in the computer hardware field. It is not difficult to envision within a few decades or less,
super computers with thousands of parallel processors. Such advances will make many of the
present computational methods obsolete. For example the parabolic approximation is made
solely to put the wave equation in a solvable form with respect to the capabilities of present
day computers. With sufficient parallel processors it is conceivable that it may be practical
to solve the full elliptic equation explicitly. We shall not dwell further on speculation about
future generations of computers. In the near term, the numerical model presented in this
report can be refined and the applications can be extended. The model is constructed in
modular form so that any new formulation for any of the component processes can easily
be incorporated into the model. The model is thus open for continual improvement.
6.1 Improved Wave Formulations
The model can be improved by better wave modeling and by a more correct formulation
of the radiation stress terms once breaking has commenced. The formulation used in this
model and previous models for the radiation stresses initiates set-up and longshore currents
at the breaker fine whereas as explained in section 5.1 experiments show otherwise.
An improved wave model will assign a non-zero value of the amplitude in the lee of
a shore parallel breakwater. Research should be done to establish a method of doing this
so as to enable more wave energy to propagate into the lee of the structure. Dalrymple
and Kirby (1988) have found a method to determine a non-zero wave height in the lee of a
breakwater. However their solution is in the form of a Fourier integral which is not suited
to the complex amplitude form required in the present model.