Large Amplitude Internal Waves of Permanent Form
- 1 February 1982
- journal article
- research article
- Published by Wiley in Studies in Applied Mathematics
- Vol. 66 (1) , 1-44
- https://doi.org/10.1002/sapm19826611
Abstract
In this paper the weakly nonlinear theory of long internal gravity waves propagating in stratified media is extended to the fully nonlinear case by treating Long's nonlinear partial differential equation for steady inviscid flows without restriction to small amplitudes and long wavelengths. The existence of finite amplitude solutions of “permanent form” is established analytically for a large class of stratification profiles, and properties are calculated numerically for the case of a hyperbolic tangent density profile in a large range of fluid depths. The numerical results agree well with the experimental data of Davis and Acrivos over the full range of wave amplitudes measured; such agreement is not obtainable with existing weakly nonlinear theories.Keywords
This publication has 24 references indexed in Scilit:
- Weakly-Nonlinear, Long Internal Gravity Waves in Stratified Fluids of Finite DepthJournal of Hydronautics, 1978
- On the speed and profile of steep solitary wavesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1976
- Generation of internal waves in the Strait of Georgia, British ColumbiaDeep Sea Research and Oceanographic Abstracts, 1976
- An integral equation for unsteady surface waves and a comment on the Boussinesq equationJournal of Fluid Mechanics, 1971
- Nonlinear boundary value problems suggested by chemical reactor theoryJournal of Differential Equations, 1970
- Solitary internal waves in deep waterJournal of Fluid Mechanics, 1967
- Internal waves of permanent form in fluids of great depthJournal of Fluid Mechanics, 1967
- The solitary wave on a stream with an arbitrary distribution of vorticityJournal of Fluid Mechanics, 1962
- On steady laminar flow with closed streamlines at large Reynolds numberJournal of Fluid Mechanics, 1956
- Détermination rigoureuse des ondes irrotationelles périodiques dans un canal à profondeur finieMathematische Annalen, 1926