Thesis-2004-Lu.pdf (12.36 MB)
Download fileNumerical simulation of internal waves in stratified fluid flow over topography
thesis
posted on 2018-09-21, 13:44 authored by Zhiming LuThe 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.]
History
School
- Science
Department
- Mathematical Sciences