Wave groups in uni-directional surface-wave models

E. van Groesen

doi:10.1007/978-94-017-1564-5_13

Wave groups in uni-directional surface-wave models

E. van Groesen

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

Abstract

Uni-directional wave models are used to study wave groups that appear in wave tanks of hydrodynamic laboratories; characteristic for waves in such tanks is that the wave length is rather small, comparable to the depth of the layer. In second-order theory, the resulting Nonlinear Schrödinger (NLS) equation for the envelope of the wave group contains the dispersion of the group velocity multiplying the linear term and a ‘gen-coefficient’ that results from mode generation multiplying the nonlinear term. The signs of these coefficients determine whether experimentally relevant wave groups are possible or not. If the dispersion is modelled in such a way that it is correct for all wave lengths for infinitesimal waves, relevant wave groups are obtained consisting of constituent waves with a certain maximal wave length; other models for the dispersion (such as in the KdV-equation) lead to different results.

Original language	English
Title of host publication	Floating, Flowing, Flying
Subtitle of host publication	Pieter J. Zandbergen’s Life as Innovator, Inspirator and Instigator in Numerical Fluid Dynamics
Editors	D. Dijkstra, B.J. Geurts, J.G.M. Kuerten, H.K. Kuiken
Place of Publication	Dordrecht
Publisher	Springer
Pages	215-226
Number of pages	12
ISBN (Electronic)	978-94-017-1564-5
ISBN (Print)	978-90-481-5049-6
DOIs	https://doi.org/10.1007/978-94-017-1564-5_13
Publication status	Published - 1998

Publication series

Name	Journal of engineering mathematics
Publisher	Springer
ISSN (Print)	0022-0833

Keywords

Wave groups
Nonlinear Schrödinger equation
Short wave dispersion
Towing tanks

Access to Document

10.1007/978-94-017-1564-5_13

Cite this

van Groesen, E. (1998). Wave groups in uni-directional surface-wave models. In D. Dijkstra, B. J. Geurts, J. G. M. Kuerten, & H. K. Kuiken (Eds.), Floating, Flowing, Flying: Pieter J. Zandbergen’s Life as Innovator, Inspirator and Instigator in Numerical Fluid Dynamics (pp. 215-226). (Journal of engineering mathematics). Springer. https://doi.org/10.1007/978-94-017-1564-5_13

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title = "Wave groups in uni-directional surface-wave models",

abstract = "Uni-directional wave models are used to study wave groups that appear in wave tanks of hydrodynamic laboratories; characteristic for waves in such tanks is that the wave length is rather small, comparable to the depth of the layer. In second-order theory, the resulting Nonlinear Schr{\"o}dinger (NLS) equation for the envelope of the wave group contains the dispersion of the group velocity multiplying the linear term and a {\textquoteleft}gen-coefficient{\textquoteright} that results from mode generation multiplying the nonlinear term. The signs of these coefficients determine whether experimentally relevant wave groups are possible or not. If the dispersion is modelled in such a way that it is correct for all wave lengths for infinitesimal waves, relevant wave groups are obtained consisting of constituent waves with a certain maximal wave length; other models for the dispersion (such as in the KdV-equation) lead to different results.",

keywords = "Wave groups, Nonlinear Schr{\"o}dinger equation, Short wave dispersion, Towing tanks",

author = "{van Groesen}, E.",

year = "1998",

doi = "10.1007/978-94-017-1564-5_13",

language = "English",

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van Groesen, E 1998, Wave groups in uni-directional surface-wave models. in D Dijkstra, BJ Geurts, JGM Kuerten & HK Kuiken (eds), Floating, Flowing, Flying: Pieter J. Zandbergen’s Life as Innovator, Inspirator and Instigator in Numerical Fluid Dynamics. Journal of engineering mathematics, Springer, Dordrecht, pp. 215-226. https://doi.org/10.1007/978-94-017-1564-5_13

Wave groups in uni-directional surface-wave models. / van Groesen, E.
Floating, Flowing, Flying: Pieter J. Zandbergen’s Life as Innovator, Inspirator and Instigator in Numerical Fluid Dynamics. ed. / D. Dijkstra; B.J. Geurts; J.G.M. Kuerten; H.K. Kuiken. Dordrecht: Springer, 1998. p. 215-226 (Journal of engineering mathematics).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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