On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime
Amplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and disper...
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doaj-a32a04b63cb14f9da1fca3551f9403852020-11-25T01:34:05ZengMDPI AGFluids2311-55212019-05-01428410.3390/fluids4020084fluids4020084On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical RegimeTakuji Waseda0Wataru Fujimoto1Amin Chabchoub2Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8563, JapanCorporate Planning Department, MS&AD InterRisk Research & Consulting, Inc., Tokyo 101-0063, JapanSchool of Civil Engineering, The University of Sydney, Sydney NSW 2006, AustraliaAmplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and dispersion parameters of optical fibers are two orders of magnitude smaller than the hydrodynamic counterparts, and therefore, considered to better assure the slowly varying envelope approximation (SVEA) of the nonlinear Schrödinger equations (NLSE). While most optics experiment demonstrate an NLSE-like symmetric solutions, experimental studies by Dudley et al. (Optics Express, 2009, 17, 21497−21508) show an asymmetric spectral evolution in the dynamics of unstable electromagnetic waves with high intensities. Motivated by this result, the hydrodynamic Euler equation is numerically solved to study the long-term evolution of a water-wave modulated wave train in the optical regime, i.e., at small steepness and spectral bandwidth. As the initial steepness is increased, retaining the initial spectral bandwidth thereby increasing the Benjamin−Feir Index, the modulation localizes, and the asymmetric and broad spectrum appears. While the deviation of the evolution from the NLSE solution is a result of broadband dynamics of free wave interaction, the resulting asymmetry of the spectrum is a consequence of the violation of the SVEA.https://www.mdpi.com/2311-5521/4/2/84hydrodynamic rogue wavesoptical rogue wavesscale separationhigh-order spectral methodnonlinear Schrödinger equation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Takuji Waseda Wataru Fujimoto Amin Chabchoub |
spellingShingle |
Takuji Waseda Wataru Fujimoto Amin Chabchoub On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime Fluids hydrodynamic rogue waves optical rogue waves scale separation high-order spectral method nonlinear Schrödinger equation |
author_facet |
Takuji Waseda Wataru Fujimoto Amin Chabchoub |
author_sort |
Takuji Waseda |
title |
On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime |
title_short |
On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime |
title_full |
On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime |
title_fullStr |
On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime |
title_full_unstemmed |
On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime |
title_sort |
on the asymmetric spectral broadening of a hydrodynamic modulated wave train in the optical regime |
publisher |
MDPI AG |
series |
Fluids |
issn |
2311-5521 |
publishDate |
2019-05-01 |
description |
Amplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and dispersion parameters of optical fibers are two orders of magnitude smaller than the hydrodynamic counterparts, and therefore, considered to better assure the slowly varying envelope approximation (SVEA) of the nonlinear Schrödinger equations (NLSE). While most optics experiment demonstrate an NLSE-like symmetric solutions, experimental studies by Dudley et al. (Optics Express, 2009, 17, 21497−21508) show an asymmetric spectral evolution in the dynamics of unstable electromagnetic waves with high intensities. Motivated by this result, the hydrodynamic Euler equation is numerically solved to study the long-term evolution of a water-wave modulated wave train in the optical regime, i.e., at small steepness and spectral bandwidth. As the initial steepness is increased, retaining the initial spectral bandwidth thereby increasing the Benjamin−Feir Index, the modulation localizes, and the asymmetric and broad spectrum appears. While the deviation of the evolution from the NLSE solution is a result of broadband dynamics of free wave interaction, the resulting asymmetry of the spectrum is a consequence of the violation of the SVEA. |
topic |
hydrodynamic rogue waves optical rogue waves scale separation high-order spectral method nonlinear Schrödinger equation |
url |
https://www.mdpi.com/2311-5521/4/2/84 |
work_keys_str_mv |
AT takujiwaseda ontheasymmetricspectralbroadeningofahydrodynamicmodulatedwavetrainintheopticalregime AT watarufujimoto ontheasymmetricspectralbroadeningofahydrodynamicmodulatedwavetrainintheopticalregime AT aminchabchoub ontheasymmetricspectralbroadeningofahydrodynamicmodulatedwavetrainintheopticalregime |
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