Forced emissions of nonlinear water waves in channels of arbitrary shape

Abstract

This thesis is a joint theoretical, numerical and experimental study concentrated on investigating the phenomenon of weakly nonlinear, weakly dispersive long water waves being generated and propagating in a channel of arbitrary cross section. The water depth and channel width are assumed comparable in size and they may vary both in time and space. Two types of theoretical models, i.e., the generalized channel Boussinesq (gcB) two-equation model and the forced channel Korteweg-de Vries (cKdV) model, are derived by using perturbation expansions for quasi-one-dimensional long waves in shallow water. In the special case for channels of variable shape and dimension but fixed in time, the motion of free traveling solitons may be calculated by our models to predict their propagation with modulated amplitude, velocity and phase. In the precence of external forcings, such as a surface pressure distribution or a submerged obstacle moving with a near critical speed, solitary waves can be produced periodically to advance upstream. Analytical solutions for three specific cross-sectional shapes, namely, the rectangular, triangular and semi-circular sections, are obtained in closed form and with the main features of the solutions examined. The specific geometry of the cross section is found to affect only the magnitude of the dispersive terms in the equations. For a submerged moving object taken as an external forcing, its effective strength of forcing is directly related to the blockage-ratio of the cross-sectional area. Our long-wave models have their useful applications to the areas of river dynamics, near-coastal engineering, and other related fields.