TABLE OF CONTENTS This chapter briefly reviews the methods available for modelling wave motion in nearshore regions based on linear wave theory. While most of the theoretical background material has been presented in the previous chapters the objective is to discuss some of the practical aspects in terms of strengths and limitations of using the methods in question.
Useful models based on linear wave theory were derived by averaging over a wave period (socalled phase averaging) and assuming locally constant depth. This lead to the classical refraction theory, ray tracing methods and the geometrical optics theory. Simply assuming locally constant depth and writing the wave motion as a product of a slowly varying amplitude and a phase function we obtained the kinematic wave model. These models all provide information about the propagation pattern of the wave motion (wave ray or wave number vector variation) and they all must be combined with an equation expressing the conservation of energy (minus various dissipative factors such as bottom friction and wave breaking) to obtain information about the wave amplitude variation. Though the theoretical basis for those methods may seem similar in that they only describe the depth refraction process they nevertheless have different properties.
Another branch of models were based on, again, the locally constant depth assumption but combined with the assumption that the wave motion can be written as a product of a slowly varying wave amplitude H( x, y) and a phase function which is given by e i?t
