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Capillary-gravity solitary waves on water of finite depth interacting with a linear shear current

Capillary-gravity solitary waves on water of finite depth interacting with a linear shear current

Gao, Tao ORCID: 0000-0002-6425-1568, Milewski, Paul and Wang, Zhan (2021) Capillary-gravity solitary waves on water of finite depth interacting with a linear shear current. Studies in Applied Mathematics. ISSN 0022-2526 (Print), 1467-9590 (Online) (In Press) (doi:https://doi.org/10.1111/sapm.12422)

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Abstract

The problem of two-dimensional capillary-gravity waves on an inviscid fluid of finite depth interacting with a linear shear current is considered. The shear current breaks the symmetry of the irrotational problem and supports simultaneously counter-propagating waves of different types: KdV-type long solitary waves and wave-packet solitary waves whose envelopes are associated with the nonlinear Schr\"odinger equation. A simple intuition for the broken symmetry is that the current modifies the Bond number differently for left- and right-propagating waves. Weakly nonlinear theories are developed in general and for two particular resonant cases: the case of second harmonic resonance and long-wave/short-wave interaction. Travelling-wave solutions and their dynamics in the full Euler equations are computed numerically using a time-dependent conformal mapping technique, and compared to some weakly nonlinear solutions. Additional attention is paid to branches of elevation generalized solitary waves of KdV type: although true embedded solitary waves are not detected on these branches, it is found that periodic wave-trains on their tails can be arbitrarily small as the vorticity increases. Excitation of waves by moving pressure distributions and modulational instabilities of the periodic waves in the resonant cases described above are also examined by the fully nonlinear computations.

Item Type: Article
Uncontrolled Keywords: solitary wave; gravity wave; capillary wave; wave interaction; surface wave
Subjects: Q Science > Q Science (General)
T Technology > T Technology (General)
Faculty / Department / Research Group: Faculty of Liberal Arts & Sciences
Faculty of Liberal Arts & Sciences > School of Computing & Mathematical Sciences (CAM)
Last Modified: 29 Jul 2021 09:59
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
Selected for REF2021: None
URI: http://gala.gre.ac.uk/id/eprint/32313

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