Propagation of obliquely incident water waves over a trench

The diffraction of obliquely incident surface waves by an asymmetric trench is investigated using linearized potential theory. A numerical solution is constructed by matching particular solutions for each subregion of constant depth along vertical boundaries ; the resulting matrix equation is solved numerically. Several cases where the trench-parallel wavenumber component in the incident-wave region exceeds the wavenumber for freely propagating waves in the trench are investigated and are found to result in large reductions in wave transmission ; however, reflection is not total owing to the finiteness of the obstacle. Results for one case are compared with data obtained from a small-scale wave-tank experiment. An approximate solution based on plane-wave modes is derived and compared with the numerical solution and, in the long-wave limit, with a previous analytic solution.