THE THEORY OF WAVE REFRACTION IN SHOALING WATER, INCLUDING THE EFFECTS OF CAUSTICS AND THE SPHERICAL EARTH,
NEW YORK UNIV BRONX GEOPHYSICAL SCIENCES LAB
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The existing wave refraction theory for surface water waves fails to predict wave behavior at and near a caustic. It is also inadequate for computing ray paths and refraction coefficients for waves traveling over large expanses of shoaling water. In the vicinity of a caustic, ray crossings occur, and the wave amplitude, according to existing theory, becomes infinite. This is, of course, devoid of physical meaning. The conventional equations for the ray path and ray separation are derived in Cartesian coordinates and therefore are valid only for a relatively small area of the ocean that can be considered as a plane surface. It is expected that considerable error in the ray patterns will occur if these equations are used for larger areas in which the curvature of the earth plays an important role. In order to overcome the first difficulty, the linearized wave equations were first modified in such a way that the bottom slope was taken into account. To solve the second problem, Fermats principle was applied directly to the spherical polar coordinate system and the equations for the ray path and ray separation were derived in terms of latitude and longitude.
- Physical and Dynamic Oceanography