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Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity

Published online by Cambridge University Press:  03 June 2019

M. Abid ,
C. Kharif Open the ORCID record for C. Kharif [Opens in a new window] ,
H.-C. Hsu  and
Y.-Y. Chen
M. Abid
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France
C. Kharif*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France
H.-C. Hsu
Affiliation:
Department of Marine Environment and Engineering, National Sun Yat-sen University, Kaohsiung, 801, Taiwan
Y.-Y. Chen
Affiliation:
Department of Marine Environment and Engineering, National Sun Yat-sen University, Kaohsiung, 801, Taiwan
*
†Email address for correspondence: kharif@irphe.univ-mrs.fr
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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.

JFM classification

Waves/Free-surface Flows: Capillary waves

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 871 , 25 July 2019 , pp. 1028 - 1043
Copyright
© 2019 Cambridge University Press 

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