Analytic Simulation To The Propagation Of Water Waves Over Finite Arrays Of Axi-symmetric Idealized Pits With Variable Depth

In this thesis, analytic modeling of the scattering of linear water waves by an array of axi-symmetric idealized pits with variable water depth is conducted. For the convenience to obtain analytic solutions, each pit is assumed to be axi-symmetric, and also idealized with the water depth profile being a power function of the radial distance r when the center of the pit is chosen as the origin of the local coordinate system with respect to the pit. Under such kind of assumption, within the inner region in each pit with variable water depth, both analytic solution in closed form to the linear long-wave equation and analytic solution in terms of Taylor series to the modified mild-slope equation can be found, while in the constant water depth region, the governing equation degenerates into the Helmholtz equation. Finally, by using matching conditions along all the pit boundaries, we can determine all the coefficients of the general solutions. The study to the scattering by an array of pits is much more difficult than that to the scattering by a single pit, since the scattering effects from all the pits will interfere for each other. This leads to great difficulty in solving the matching conditions. The present series solution not only extends both the analytic solutions to the long-wave equation and the modified mild-slope equation, but also extends the analytic solution for scattering by an array of bottom-mounted cylinders, that is to say, all these solutions are just the special cases of our new solution. Based on the present solution, the influence of the incident angle,the total number of pits and the size of each pit on the wave amplification is analyzed.