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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Bibliographic Details
Published inJournal of fluid mechanics Vol. 871; pp. 1028 - 1043
Main Authors Abid, M., Kharif, C., Hsu, H.-C., Chen, Y.-Y.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 25.07.2019
Cambridge University Press (CUP)
Subjects
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
capillary waves
transverse instability
NLS equation
vorticity
gravity-capillary solitary waves
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Summary: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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.350