Numerical simulation of internal waves in stratified fluid flow over topography

The main purpose of this thesis is to investigate internal solitary wave generation and evolution in density-stratified fluid flows over both two-dimensional and three-dimensional bottom topographies using mainly numerical methods supported by some theoretical results. The numerical scheme to solve the forced KdV, KPII and KPI equation is a combination of the Runge–Kutta and Crank–Nicholson methods; a pseudo-spectral method is used to solve the two-dimensional fully nonlinear Euler equations in the streamfunction-vorticity form. The numerical results for a stratified flow over a two-dimensional step or an obstacle show that, in the resonant region, a forward step mainly generates upstream-advancing waves, while a backward step mainly generates downstream-propagating waves (a depression followed by lee waves), so the waves generated by a localised positive obstacle can be regarded as a simple superposition of the waves generated by its fore part and aft part. In contrast, the waves generated by a negative obstacle are quite different due to the nonlinear interaction between waves generated by its fore part and aft part. [Continues.]