Refraction of water waves by islands and shoals with circular bottom‐contours

Abstract

The bending of water waves by islands and shoals with circular bottom‐contours is Investigated from an analytical standpoint to obtain a precise determination of resulting wave‐patterns and wave‐heights. SNELL'S law of refraction is assumed, and FERMAT'S law or the principle of least time therefore applies. Application of FERMAT'S law and of the established relation between wave‐velocity and depth of water enables determinations of lines orthogonal to tho wave crests for various types of contour gradients. Five different cases are discussed. It is shown that for certain contour gradients, islands have no shore protected from high waves. A shoal is characterized by the dividing of a single crest Into two crests. Height variation along refracted crests at considerable distances beyond an island is shown to bo critically dependent upon contour gradient.