Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity
The bifurcation of two-dimensional gravity–capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant vorticity. We found that gravity–capillary solitary waves with decaying oscillatory tails exist in deep water in the...
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| Published in | Journal of fluid mechanics Vol. 871; pp. 1028 - 1043 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
25.07.2019
Cambridge University Press (CUP) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-1120 1469-7645 |
| DOI | 10.1017/jfm.2019.350 |
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| Abstract | The bifurcation of two-dimensional gravity–capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant vorticity. We found that gravity–capillary solitary waves with decaying oscillatory tails exist in deep water in the presence of vorticity. Furthermore we found that the presence of vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the vorticity. |
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| AbstractList | The bifurcation of two-dimensional gravity–capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant vorticity. We found that gravity–capillary solitary waves with decaying oscillatory tails exist in deep water in the presence of vorticity. Furthermore we found that the presence of vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the vorticity. |
| Author | Abid, M. Chen, Y.-Y. Kharif, C. Hsu, H.-C. |
| Author_xml | – sequence: 1 givenname: M. surname: Abid fullname: Abid, M. organization: Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France – sequence: 2 givenname: C. orcidid: 0000-0003-0716-8183 surname: Kharif fullname: Kharif, C. email: kharif@irphe.univ-mrs.fr organization: Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France – sequence: 3 givenname: H.-C. surname: Hsu fullname: Hsu, H.-C. organization: Department of Marine Environment and Engineering, National Sun Yat-sen University, Kaohsiung, 801, Taiwan – sequence: 4 givenname: Y.-Y. surname: Chen fullname: Chen, Y.-Y. organization: Department of Marine Environment and Engineering, National Sun Yat-sen University, Kaohsiung, 801, Taiwan |
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| Cites_doi | 10.4310/CMS.2005.v3.n1.a6 10.1063/1.858626 10.1063/1.869315 10.1017/jfm.2017.50 10.1017/S002211208900073X 10.1007/s10665-011-9493-1 10.1017/S0022112005005136 10.1063/1.862364 10.1017/jfm.2016.639 10.1145/365723.365727 10.1098/rspa.2006.1670 10.1137/090758386 10.1017/S0022112005005823 10.1111/j.1467-9590.2009.00432.x 10.1098/rspa.2013.0537 10.1017/S0022112010005999 10.1017/jfm.2016.658 10.1017/S0022112092000193 10.1007/978-3-642-83876-7 10.1017/jfm.2018.627 10.1007/s10665-006-9122-6 10.1016/S0997-7546(99)80035-1 10.1017/S0022112079000835 10.1007/BF00203041 10.1088/0031-8949/40/2/008 10.1017/S0022112095001236 10.1017/jfm.2012.320 10.1137/0914038 10.1017/S0022112093003945 |
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| Keywords | capillary waves transverse instability NLS equation vorticity gravity-capillary solitary waves |
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| Snippet | The bifurcation of two-dimensional gravity–capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in... The bifurcation of two-dimensional gravity-capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in... |
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| SubjectTerms | Bifurcations Capillary waves Deep water Fluid mechanics Gravitation Gravity Group velocity Growth rate Instability Investigations JFM Papers Mechanics Phase velocity Physics Solitary waves Stability Stability analysis Velocity Vorticity Wave properties |
| Title | Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity |
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