An Analytical Model of Periodic Waves in Shallow Water - Summary,

Abstract : An explicit, analytical model is presented of finite amplitude waves in shallow water. The waves in question have two independent spatial periods, in two independent horizontal directions. Both short-crested and long-crested waves are available from the model. Every wave pattern is an exact solution of the Kadomtsev-Petviashvili equation, and is based on a Riemann theta function of genus 2. These bi-periodic waves are direct generalizations of the well-known (simply periodic) cnoidal waves. Just as cnoidal waves are often used as one-dimensional models of typical nonlinear, periodic waves in shallow water, these bi-periodic waves may be considered to represent typical nonlinear, periodic waves in shallow water without the assumption of one-dimensionality. (Author)