TABLE OF CONTENTS Up to this point, we have explored the solution to the linearized wave problem on a constant depth. This has lead to determination of essentially all the mechanical properties of the linear wave solution, from propagation speed to velocity and pressure field, and including instantaneous properties as well as depth integrated, time averaged properties.
However, an important limitation of all investigations and results so far has been the assumption of constant water depth and one horizontal dimension (also called 1-D horizontal (1DH) motion or 2-D vertical (2DV) motion).
In the situations encountered in nature, these simplifications are hardly ever satisfied: In practice the depth varies from point to point and the wave motion changes accordingly.
Therefore, it is important to examine to which extent the linear wave theory we have developed can be extended to the more general situations of varying depth and the propagation of the waves in a 2DH domain. This is the objective of the next three sections. The linear wave models described later in Chapter 6 are essentially also based on the results which we will develop in these sections. Therefore they are also subject to the same idealizations and limitations.
In short, we are planning to look at the following generalizations
Refraction of waves in the horizontal plane (2DH) in regions with varying water depth (depth refraction) (section 3.5).
The modification of waves by currents (section 3.6).
Wave propagation in 2DH regions with varying depth...
