Large fully nonlinear solitary and solitary-like internal waves in the ocean

Abstract

In this thesis we study fully nonlinear internal waves in a stratified ocean. These waves are isolated disturbances that do not change form as they propagate horizontally along the waveguide of the density stratified ocean. After surveying semi-analytical asymptomatic theories for small, finite amplitude waves we present a variational technique for calculating large, fully nonlinear internal solitary waves which are exact solutions of the Euler equations governing an inviscid fluid. This technique is subsequently used to discuss the effect of horizontal background currents on solitary wave properties. Particular attention is paid to upper bounds on the solitary wave amplitude. Next we discuss one way the variational algorithm can be used to compute solitary-like waves which are past breaking, and the properties of such solitary wave-like objects. Finally we consider the interaction of an initially solitary wave with a viscous boundary layer. We show that for cases in which vorticity is produced in the boundary layer upstream of the wave, for example due to an appropriately chosen background current, this interaction can lead to the instability of the solitary wave and can result in significant transport of sediment out of the bottom boundary layer into the main water column.