Nonconservative higher-order hydrodynamic modulation instability.
Identifieur interne : 000716 ( Main/Exploration ); précédent : 000715; suivant : 000717Nonconservative higher-order hydrodynamic modulation instability.
Auteurs : O. Kimmoun [France] ; H C Hsu [Taïwan] ; B. Kibler [France] ; A. Chabchoub [Finlande]Source :
- Physical review. E [ 2470-0053 ] ; 2017.
Abstract
The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy sidebands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary sidebands generate an infinite number of additional sidebands, forming a triangular sideband cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive sideband pair that is created is also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirms observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counterintuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids, and plasma.
DOI: 10.1103/PhysRevE.96.022219
PubMed: 28950632
Affiliations:
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Kimmoun</name><affiliation wicri:level="3"><nlm:affiliation>Aix-Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille, France.</nlm:affiliation><country xml:lang="fr">France</country><wicri:regionArea>Aix-Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille</wicri:regionArea><placeName><region type="region">Provence-Alpes-Côte d'Azur</region><region type="old region">Provence-Alpes-Côte d'Azur</region><settlement type="city">Marseille</settlement></placeName></affiliation></author><author><name sortKey="Hsu, H C" sort="Hsu, H C" uniqKey="Hsu H" first="H C" last="Hsu">H C Hsu</name><affiliation wicri:level="1"><nlm:affiliation>Department of Marine Environment and Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan.</nlm:affiliation><country xml:lang="fr">Taïwan</country><wicri:regionArea>Department of Marine Environment and Engineering, National Sun Yat-Sen University, Kaohsiung</wicri:regionArea><wicri:noRegion>Kaohsiung</wicri:noRegion></affiliation></author><author><name sortKey="Kibler, B" sort="Kibler, B" uniqKey="Kibler B" first="B" last="Kibler">B. Kibler</name><affiliation wicri:level="1"><nlm:affiliation>Laboratoire Interdisciplinaire Carnot de Bourgogne-UMR 6303 CNRS/Université Bourgogne Franche-Comté, 21078 Dijon, France.</nlm:affiliation><country xml:lang="fr">France</country><wicri:regionArea>Laboratoire Interdisciplinaire Carnot de Bourgogne-UMR 6303 CNRS/Université Bourgogne Franche-Comté, 21078 Dijon</wicri:regionArea><wicri:noRegion>21078 Dijon</wicri:noRegion><wicri:noRegion>21078 Dijon</wicri:noRegion></affiliation></author><author><name sortKey="Chabchoub, A" sort="Chabchoub, A" uniqKey="Chabchoub A" first="A" last="Chabchoub">A. Chabchoub</name><affiliation wicri:level="4"><nlm:affiliation>Department of Mechanical Engineering, Aalto University, 02150 Espoo, Finland.</nlm:affiliation><country xml:lang="fr">Finlande</country><wicri:regionArea>Department of Mechanical Engineering, Aalto University, 02150 Espoo</wicri:regionArea><orgName type="university">Université Aalto</orgName><placeName><settlement type="city">Espoo</settlement><region type="région" nuts="2">Uusimaa</region></placeName></affiliation></author></analytic><series><title level="j">Physical review. E</title><idno type="eISSN">2470-0053</idno><imprint><date when="2017" type="published">2017</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy sidebands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary sidebands generate an infinite number of additional sidebands, forming a triangular sideband cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive sideband pair that is created is also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirms observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counterintuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids, and plasma.</div></front></TEI><affiliations><list><country><li>Finlande</li><li>France</li><li>Taïwan</li></country><region><li>Provence-Alpes-Côte d'Azur</li><li>Uusimaa</li></region><settlement><li>Espoo</li><li>Marseille</li></settlement><orgName><li>Université Aalto</li></orgName></list><tree><country name="France"><region name="Provence-Alpes-Côte d'Azur"><name sortKey="Kimmoun, O" sort="Kimmoun, O" uniqKey="Kimmoun O" first="O" last="Kimmoun">O. Kimmoun</name></region><name sortKey="Kibler, B" sort="Kibler, B" uniqKey="Kibler B" first="B" last="Kibler">B. Kibler</name></country><country name="Taïwan"><noRegion><name sortKey="Hsu, H C" sort="Hsu, H C" uniqKey="Hsu H" first="H C" last="Hsu">H C Hsu</name></noRegion></country><country name="Finlande"><region name="Uusimaa"><name sortKey="Chabchoub, A" sort="Chabchoub, A" uniqKey="Chabchoub A" first="A" last="Chabchoub">A. Chabchoub</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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