Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory
Coherent wave groups are not only characterized by the intrinsic shape of the wave packet, but also by the underlying phase evolution during the propagation. Exact deterministic formulations of hydrodynamic or electromagnetic coherent wave groups can be obtained by solving the nonlinear Schrödinger...
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doaj-468908c938f747388e873635753e647d2021-09-26T00:08:33ZengMDPI AGFluids2311-55212021-08-01630830810.3390/fluids6090308Phase Evolution of the Time- and Space-Like Peregrine Breather in a LaboratoryYuchen He0Pierre Suret1Amin Chabchoub2Centre for Wind, Waves and Water, School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, AustraliaUniv. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, FranceCentre for Wind, Waves and Water, School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, AustraliaCoherent wave groups are not only characterized by the intrinsic shape of the wave packet, but also by the underlying phase evolution during the propagation. Exact deterministic formulations of hydrodynamic or electromagnetic coherent wave groups can be obtained by solving the nonlinear Schrödinger equation (NLSE). When considering the NLSE, there are two asymptotically equivalent formulations, which can be used to describe the wave dynamics: the time- or space-like NLSE. These differences have been theoretically elaborated upon in the 2016 work of Chabchoub and Grimshaw. In this paper, we address fundamental characteristic differences beyond the shape of wave envelope, which arise in the phase evolution. We use the Peregrine breather as a referenced wave envelope model, whose dynamics is created and tracked in a wave flume using two boundary conditions, namely as defined by the time- and space-like NLSE. It is shown that whichever of the two boundary conditions is used, the corresponding local shape of wave localization is very close and almost identical during the evolution; however, the respective local phase evolution is different. The phase dynamics follows the prediction from the respective NLSE framework adopted in each case.https://www.mdpi.com/2311-5521/6/9/308nonlinear wavesPeregrine breatherrogue wavespattern formation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yuchen He Pierre Suret Amin Chabchoub |
spellingShingle |
Yuchen He Pierre Suret Amin Chabchoub Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory Fluids nonlinear waves Peregrine breather rogue waves pattern formation |
author_facet |
Yuchen He Pierre Suret Amin Chabchoub |
author_sort |
Yuchen He |
title |
Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory |
title_short |
Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory |
title_full |
Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory |
title_fullStr |
Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory |
title_full_unstemmed |
Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory |
title_sort |
phase evolution of the time- and space-like peregrine breather in a laboratory |
publisher |
MDPI AG |
series |
Fluids |
issn |
2311-5521 |
publishDate |
2021-08-01 |
description |
Coherent wave groups are not only characterized by the intrinsic shape of the wave packet, but also by the underlying phase evolution during the propagation. Exact deterministic formulations of hydrodynamic or electromagnetic coherent wave groups can be obtained by solving the nonlinear Schrödinger equation (NLSE). When considering the NLSE, there are two asymptotically equivalent formulations, which can be used to describe the wave dynamics: the time- or space-like NLSE. These differences have been theoretically elaborated upon in the 2016 work of Chabchoub and Grimshaw. In this paper, we address fundamental characteristic differences beyond the shape of wave envelope, which arise in the phase evolution. We use the Peregrine breather as a referenced wave envelope model, whose dynamics is created and tracked in a wave flume using two boundary conditions, namely as defined by the time- and space-like NLSE. It is shown that whichever of the two boundary conditions is used, the corresponding local shape of wave localization is very close and almost identical during the evolution; however, the respective local phase evolution is different. The phase dynamics follows the prediction from the respective NLSE framework adopted in each case. |
topic |
nonlinear waves Peregrine breather rogue waves pattern formation |
url |
https://www.mdpi.com/2311-5521/6/9/308 |
work_keys_str_mv |
AT yuchenhe phaseevolutionofthetimeandspacelikeperegrinebreatherinalaboratory AT pierresuret phaseevolutionofthetimeandspacelikeperegrinebreatherinalaboratory AT aminchabchoub phaseevolutionofthetimeandspacelikeperegrinebreatherinalaboratory |
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