Incoming water waves against an overhanging cliff

摘要

A reduction technique is utilized to determine the exact solution to the boundary value problem involving the two-dimensional Laplace equation in an angular region, of vertical angle 45°. The associated physical problem is that of determining the effect of an incoming surface water wave, against a overhanging cliff in the form of a rigid plane inclinded at an angle of 45° to the vertical. It is shown that two distinct classes of solutions are possible. One of these solutions possesses a source-like behaviour at the corner point ( i.e., at the shore-line ) whilst the other is regular at the corner point but involves reflected wave terms. The exact expression for the complex reflection coefficient is determined for the second class of solution.