Kelvin-wave diffraction by a gap

Abstract

The problem of diffraction of a Kelvin wave by a narrow opening in a barrier separating two semi-infinite sheets of water is formulated as an integral equation. An approximate solution is obtained on the hypothesis that the gap is small compared with the length of the incident wave. The scattered disturbance comprises both Kelvin and Poincaré waves, and asymptotic formulate for their amplitudes are obtained. The results, which are relevant to tidal diffraction by a strait, reveal that the phase shift in the diffracted Kelvin wave is much larger than the corresponding shift induced by either a narrow channel or an inland sea opening into a semi-infinite ocean.