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Nonlinear waves and solitons in water

Wu, Theodore Yaotsu (1998) Nonlinear waves and solitons in water. Physica D, 123 (1-4). pp. 48-63. ISSN 0167-2789. https://resolver.caltech.edu/CaltechAUTHORS:20200306-150642432

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Abstract

A new theoretical model is introduced for evaluating three-dimensional gravity-capillary waves in water of uniform depth to various degrees of validity for predicting nonlinear dispersive water wave phenomena. It is first based on two basic equations, one being the continuity equation averaged over the water depth, and the other the horizontal projection of the momentum equation at the free surface. These two partial differential equations are both exact (for flows assumed incompressible and inviscid), but involve three unknowns: the horizontal velocity at the free surface (in two horizontal dimensions), û; the depth-mean horizontal velocity, u; and the water surface elevation, ξ. Clsure of the system for modeling fully nonlinear and fully dispersive water waves is accomplished by finding for the velocity field a third exact equation relating these unknowns. Interesting phenomena in various cases are illustrated with review and discussion of literature.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/s0167-2789(98)00111-0DOIArticle
Additional Information:© 1998 Published by Elsevier. The author appreciates having interesting discussions with Jin Zhang, Wooyoung Choi, Roberto Camassa and Michelle Teng, and would like to thank Wendong Qu for the good assistance provided. He is also indebted to a referee for pointing out one recent publication with which equation (12gs) conforms. This study has been supported by NSF through the Hazard Mitigation Program under Grant CMS-9503620.
Funders:
Funding AgencyGrant Number
NSFCMS-9503620
Subject Keywords:Nonlinear water waves; Soliton street; Wave collisions; Variable channels; Wave models
Issue or Number:1-4
Record Number:CaltechAUTHORS:20200306-150642432
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200306-150642432
Official Citation:Theodore Yaotsu Wu, Nonlinear waves and solitons in water, Physica D: Nonlinear Phenomena, Volume 123, Issues 1–4, 1998, Pages 48-63, ISSN 0167-2789, https://doi.org/10.1016/S0167-2789(98)00111-0.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101758
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:06 Mar 2020 23:31
Last Modified:06 Mar 2020 23:31

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