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Article: Internal rogue waves in stratified flows and the dynamics of wave packets

TitleInternal rogue waves in stratified flows and the dynamics of wave packets
Authors
KeywordsStratified flows
Schrödinger systems
Rogue waves
Issue Date2018
PublisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/nonrwa
Citation
Nonlinear Analysis: Real World Applications, 2018, v. 44, p. 449-464 How to Cite?
AbstractA theoretical study on the occurrence of internal rogue waves in density stratified flows is conducted. While internal rogue waves for long wave models have been studied in the literature, the focus here is on unexpectedly large amplitude displacements arising from the propagation of slowly varying wave packets. In the first stage of the analysis we calculate new exact solutions of the linear modal equations in a finite domain for realistic stratification profiles. These exact solutions are then used to facilitate the calculations of the second harmonic and the induced mean motion, leading to a nonlinear Schrödinger equation for the evolution of a wave packet. The dispersion and nonlinear coefficients then determine the likelihood for the occurrence of rogue waves. Several cases of buoyancy frequency (N) are investigated. For N2 profiles of hyperbolic secant form, rogue waves are unlikely to occur as the dispersion and nonlinear coefficients are of opposite signs. For N2 taking constant values, rogue waves will arise for reasonably small carrier envelope wavenumbers, in sharp contrast with the situation for a free surface, where the condition is kh > 1.363 (k = wavenumber of the carrier envelope, h = depth). Finally, a special N2 profile permits an analytical treatment for a linear shear current. Unexpectedly large amplitude waves are possible as the dispersion and nonlinear coefficients can then be of the same sign. © 2018 Elsevier Ltd
Persistent Identifierhttp://hdl.handle.net/10722/271233
ISSN
2019 Impact Factor: 2.072
2015 SCImago Journal Rankings: 1.792

 

DC FieldValueLanguage
dc.contributor.authorLiu, T-
dc.contributor.authorChan, HN-
dc.contributor.authorGrimshaw, RHJ-
dc.contributor.authorChow, KW-
dc.date.accessioned2019-06-24T01:05:55Z-
dc.date.available2019-06-24T01:05:55Z-
dc.date.issued2018-
dc.identifier.citationNonlinear Analysis: Real World Applications, 2018, v. 44, p. 449-464-
dc.identifier.issn1468-1218-
dc.identifier.urihttp://hdl.handle.net/10722/271233-
dc.description.abstractA theoretical study on the occurrence of internal rogue waves in density stratified flows is conducted. While internal rogue waves for long wave models have been studied in the literature, the focus here is on unexpectedly large amplitude displacements arising from the propagation of slowly varying wave packets. In the first stage of the analysis we calculate new exact solutions of the linear modal equations in a finite domain for realistic stratification profiles. These exact solutions are then used to facilitate the calculations of the second harmonic and the induced mean motion, leading to a nonlinear Schrödinger equation for the evolution of a wave packet. The dispersion and nonlinear coefficients then determine the likelihood for the occurrence of rogue waves. Several cases of buoyancy frequency (N) are investigated. For N2 profiles of hyperbolic secant form, rogue waves are unlikely to occur as the dispersion and nonlinear coefficients are of opposite signs. For N2 taking constant values, rogue waves will arise for reasonably small carrier envelope wavenumbers, in sharp contrast with the situation for a free surface, where the condition is kh > 1.363 (k = wavenumber of the carrier envelope, h = depth). Finally, a special N2 profile permits an analytical treatment for a linear shear current. Unexpectedly large amplitude waves are possible as the dispersion and nonlinear coefficients can then be of the same sign. © 2018 Elsevier Ltd-
dc.languageeng-
dc.publisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/nonrwa-
dc.relation.ispartofNonlinear Analysis: Real World Applications-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectStratified flows-
dc.subjectSchrödinger systems-
dc.subjectRogue waves-
dc.titleInternal rogue waves in stratified flows and the dynamics of wave packets-
dc.typeArticle-
dc.identifier.emailChow, KW: kwchow@hku.hk-
dc.identifier.authorityChow, KW=rp00112-
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.nonrwa.2018.05.015-
dc.identifier.scopuseid_2-s2.0-85048531848-
dc.identifier.hkuros298072-
dc.identifier.volume44-
dc.identifier.spage449-
dc.identifier.epage464-
dc.publisher.placeUnited Kingdom-

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