energy flux is conserved between two adjacent rays. As a consequence of this assumption,

ray theory breaks down when wave ray crossings and caustics occur because the physics

of diffraction are totally ignored in the numerical ray models.

Starting in the early 1980' , coastal designers and researchers have recognized the

s

importance of the combined effects of refraction and diffraction and begun to develop

improved theories and associated numerical models.

There are indeed several wave

theories available that could adequately describe the combined refraction and diffraction of

waves from deep water to shallow water (Demirbilek and Webster 1992 and 1998). One

of these is the mild-slope equation (MSE). This is a depth-averaged, elliptic type partial

differential equation which ignores the evanescent modes (locally emanated waves) and

assumes that the rate of change of depth and current within a wavelength is small, hence

the ` ild-slope'acronym.

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Numerous MSE-based numerical models have been developed for predicting the

wave forces on offshore structures and studying wave fields around the offshore islands.

Numerical, laboratory and filed tests of the NSE models have shown that the MSE can

provide accurate solutions to problems where the bottom slope is up to 1:3. From a

practical standpoint, the computational requirements for solving the MSE are munch

larger than those for ray tracing. The reasons for this are because the MSE is a two-

dimensional equation and has to be solved as a boundary-value problem with appropriate

boundary conditions.

The entire domain of interest must be discretized and solved

simultaneously and the element size has to be small enough that there are about 10 to 15

nodes within each wavelength. These requirements place severe demands on computer

resources when applying MSE models to large coastal domains.

A difficult problem in the prediction of waves near shore is to determine where

approximately the wave breaking (and breaker line) occurs when waves are inside the sure

zone. In numerical models presently used, this location is not known a priori, and is

usually selected with an ad hoc criteria based on the ratio of wave height to local water

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