Spectra of Water Waves in Channels and around Islands

Abstract

Spectra of bounded and unbounded basins are calculated on an asymptotic approximation based on smallness of the seabed slopes. This leads to the geometrical optics theory of surface waves of Keller, which is used to extend the known, exact result for an idealized beach to the prediction of the spectra of a variety of more natural water bodies. Attention is directed to cylindrically symmetrical and two-dimensional topographies corresponding, respectively, to islands and to continental slopes and laboratory channels. Marked differences are found in the character of the spectra for these two types of topography.