Diffraction of Kelvin waves from a rotating channel with an infinite and a semi-infinite barrier

Abstract

The diffraction of long waves in a rotating channel of constant depth, consisting of an infinite and a semi-infinite parallel barrier of zero thickness, is investigated. The excitation is due to a Kelvin wave travelling towards the open end from inside the channel. An exact solution is given for the region inside the semi-infinite channel, consisting of a 'reflected' Kelvin wave and the various travelling modes, which become attenuated waves when the width of the channel is less than a certain value. MOreover it is shown that there is a resonance effect for some critical values of the channel width. In the remaining region an asymptotic expression for the far field is obtained. This expression involves a Kelvin wave travelling along the infinite barrier and also an outgoing cylindrical wave (Poincare wave) coming from the edge of the semi-infinite barrier of the channel.