Wave propagation across the continental shelf

Abstract

Wave propagation across the continental shelf is studied by analogy with transmission-line theory. Fourier transformation along the contours of constant depth, which are assumed parallel to a straight coastline, yields a Sturm-Liouville equation for a prescribed depth profile h(x). The modal spectrum of the profile, which comprises a finite, discrete spectrum of trapped modes and a continuous spectrum of radiated modes, is established. The Green's function for a point source on the coastline is constructed by Fourier superposition over this spectrum. Detailed results are calculated for a two-step model (level shelf separated from level abyss by vertical cliff) and for a gradually sloping shelf that merges smoothly into a level abyss. The radiation impedance of a harbour is calculated, and the effects of the continental shelf on the resonant response of the harbour to a tsunami are discussed.