Numerical computation of steep gravity waves in shallow water
- 1 October 1979
- journal article
- conference paper
- Published by AIP Publishing in Physics of Fluids
- Vol. 22 (10) , 1868-1871
- https://doi.org/10.1063/1.862492
Abstract
An efficient numerical scheme to compute steep gravity waves in water of shallow uniform depth is described. The problem is formulated as a system of integrodifferential equations for the free surface. A numerical procedure based on Newton’s iterations is devised to solve these equations. Solutions of high accuracy for depth as small as 1/120 of a wavelength are presented. Numerical confirmation is obtained for the existence of maxima of the potential and kinetic energies of the waves as functions of the steepness.Keywords
This publication has 6 references indexed in Scilit:
- Theory of the almost-highest wave. Part 2. Matching and analytic extensionJournal of Fluid Mechanics, 1978
- Steep gravity waves in water of arbitrary uniform depthPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1977
- On the speed and profile of steep solitary wavesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1976
- Integral properties of periodic gravity waves of finite amplitudeProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1975
- On the mass, momentum, energy and circulation of a solitary wave. IIProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1974
- Computer extension and analytic continuation of Stokes’ expansion for gravity wavesJournal of Fluid Mechanics, 1974