Analytical Simulation Of Oscillations In Coupled Basins With Variable Water Depths

It is well-known that a harbor can be agitated into oscillated state due to the fact that incident waves arriving at a depth increase or decrease are partially re?ected. Such oscillation may excite large motions in mooring system leading mooring lines to break and ships to collide with adjacent structures.The mathematical model of the harbor oscillation is involved with boundary valued problems of partial di?erential equations and the related analytical solutions are few.A very few previous solutions are restricted either to constant water depth or piecewise constant water depth or in?nite deep water depth, either to one-dimensional model,either to a single harbor.In this thesis, the oscillation occurred in a single harbor is ?rstly studied. Within the interior of the harbor, the two-dimensional rather than one-dimensional long-wave equation is adopted as the governing equation. It is obvious that the two-dimensional equation matches the harbor shape much better than the one-dimensional equation does. By using the method of variable separation, the partial di?erential equation is transformed into two ordinary di?erential equations, which are successfully solved and matched with the solution in the outer sea. The ?nal solution of the oscillation factor coincides well with experimental data for the harbor with ?at bottom.Second, the oscillation occurred in a harbor with couple basins by incident long waves is also studied, where the two basins are connected by a narrow channel. An analytical solution to the two-dimensional long-wave equation for the oscillation factor is constructed. Based on the solution, the in?uence of various parameters of the harbor including the length of the middle channel on the oscillation factor is investigated.