An analytical model of periodic waves in shallow water
Abstract
An analytical model is presented of finite amplitude waves in shallow water. The waves discussed have two independent spatial periods, in two independent horizontal directions. Both short-crested and long-crested waves are available from the model, and every wave pattern is an identical solution of the Kadomtsev-Petviashvili equation, 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.
- Publication:
-
NASA STI/Recon Technical Report N
- Pub Date:
- 1984
- Bibcode:
- 1984STIN...8516086S
- Keywords:
-
- Amplitudes;
- Cnoidal Waves;
- Periodic Functions;
- Shallow Water;
- Dimensions;
- Mathematical Models;
- Nonlinear Systems;
- Patterns;
- Solutions;
- Fluid Mechanics and Heat Transfer