Orthogonal coordinates for the analysis of long gravity waves near islands

Abstract

A method is presented for the evaluation of an orthogonal coordinate system of particular use in the study of the diffraction of long gravity waves near islands of irregular shape. The problem involves a conformal mapping of the island onto a coordinate plane in which the island contour is a unit circle. The mapping relation is evaluated by an iterative procedure which is reminiscent of a method introduced by Theodorsen, but has the advantage that it is applicable to an island contour in which the island contour relation r(9) , in polar coordinates, is multivalued for a given range of 9. This generality is achieved by employing a parametric representation of the island contour in which the arc length on the island contour enters as the parameter. Application is made for two specific cases, Wake Island and Kauai.