An analytical model of periodic waves in shallow water
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 shortcrested and longcrested waves are available from the model. Every wave pattern is an exact solution of the KadomtsevPetviashvill equation, and is based on a Riemann theta function of genus 2. These biperiodic waves are direct generalizations of the wellknown (simply periodic) cnoidal waves. Just as cnoidal waves are often used as onedimensional models of typical nonlinear, periodic waves in shallow water, these biperiodic waves may be considered to represent typical nonlinear, periodic waves in shallow water without the assumption of onedimensionality.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1984
 Bibcode:
 1984STIN...8516085S
 Keywords:

 Amplitudes;
 Cnoidal Waves;
 Periodic Functions;
 Shallow Water;
 Dimensions;
 Equations;
 Mathematical Models;
 Nonlinear Systems;
 Solutions;
 Fluid Mechanics and Heat Transfer