On functional equations leading to analytical solutions of internal waves

Abstract

This master thesis deals with the construction of analytical solutions to smallamplitude internal gravity waves. In the first part analytical solutions to internal waves in inviscid and uniformly stratified fluids confined to a two-dimensional trapezoid are constructed. The new method by which these exact solutions are constructed gives new insight into the complex self-similar structure of the velocity f ield. In the second part the generation of internal waves in a uniformly stratified ocean by barotropic flow over irregular topography is described. Exact solutions to the internal wave field derived from solutions to Abel’s functional equation are presented for a finite support bottom topography which lacks tidal conversion for a specific barotropic tidal frequency.