Seminar

In this talk, we will study two classical problems of linear water waves with

varying depth. One problem is related to normal modes for the linear water wave problem

on infinite straight channels of constant cross-section. The second problem is about

trapped waves, that is, the phenomenon whereby waves can remain confined in some

region of the fluid domain. Here we will discuss the wave trapping problem associated

with continental shelves by way of a simple model such as a rectangular shelf. It is

important to point out that for problem one only a few special solutions are known. For

problem two, no exact solutions are known but there is a simplified approach in which is

possible to find that eigenfrequencies exist which correspond to modes trapped over the

shelf. These modes are analogous to the so-called bound states in a square-well potential

in quantum mechanics. The main motivation of choosing these problems that involve

depth geometries and models with known exact results was to test simplifications of the

lowest order variable depth Dirichlet-Neumann operator for variable depth.