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Two-dimensional gravity–capillary solitary waves on deep water: generation and transverse instability

Published online by Cambridge University Press:  17 November 2017

Beomchan Park  and
Yeunwoo Cho Open the ORCID record for Yeunwoo Cho [Opens in a new window]
Beomchan Park
Affiliation:
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehakro, Yuseonggu, Daejeon,  34141, Republic of Korea
Yeunwoo Cho*
Affiliation:
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehakro, Yuseonggu, Daejeon,  34141, Republic of Korea
*
†Email address for correspondence: ywoocho@kaist.ac.kr
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Abstract

Two-dimensional (2-D) gravity–capillary solitary waves are generated using a moving pressure jet from a 2-D narrow slit as a forcing onto the surface of deep water. The forcing moves horizontally over the surface of the deep water at speeds close to the minimum phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$. Four different states are observed according to the forcing speed. At relatively low speeds below $c_{min}$, small-amplitude depressions are observed and they move steadily just below the moving forcing. As the forcing speed increases towards $c_{min}$, nonlinear 2-D gravity–capillary solitary waves are observed, and they move steadily behind the moving forcing. When the forcing speed is very close to $c_{min}$, periodic shedding of a 2-D local depression is observed behind the moving forcing. Finally, at relatively high speeds above $c_{min}$, a pair of short and long linear waves is observed, respectively ahead of and behind the moving forcing. In addition, we observe the transverse instability of free 2-D gravity–capillary solitary waves and, further, the resultant formation of three-dimensional gravity–capillary solitary waves. These experimental observations are compared with numerical results based on a model equation that admits gravity–capillary solitary wave solutions near $c_{min}$. They agree with each other very well. In particular, based on a linear stability analysis, we give a theoretical proof for the transverse instability of the 2-D gravity–capillary solitary waves on deep water.

JFM classification

Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 834 , 10 January 2018 , pp. 92 - 124
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Copyright
© 2017 Cambridge University Press 

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