Fourth-order stability analysis for capillary-gravity waves on finite-depth currents with constant vorticity

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Author(s)Dhar, A. K.
Author(s)Kirby, James T.
Date Accessioned2023-04-05T14:52:46Z
Date Available2023-04-05T14:52:46Z
Publication Date2023-02-01
DescriptionThis article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in A. K. Dhar and James T. Kirby , "Fourth-order stability analysis for capillary-gravity waves on finite-depth currents with constant vorticity", Physics of Fluids 35, 026601 (2023) https://doi.org/10.1063/5.0136002 and may be found at https://doi.org/10.1063/5.0136002. This article will be embargoed until 02/01/2024.
AbstractWe derive a fourth-order nonlinear evolution equation (NLEE) for narrow-banded Stokes wave in finite depth in the presence of surface tension and a mean flow with constant vorticity. The two-dimensional capillary-gravity wave motion on the surface of finite depth is considered here. The analysis is limited to one horizontal dimension, parallel to the direction of wave propagation, in order to take advantage of a formulation using potential flow theory. This evolution equation is then employed to examine the effect of vorticity on the Benjamin–Feir instability (BFI) of the Stokes capillary-gravity wave trains. It is found that the vorticity modifies significantly the modulational instability and in the case of finite depth, the combined effect of vorticity and capillarity is to enhance the instability growth rate influenced by capillarity when the vorticity is negative. The key point is that the present fourth-order analysis exhibits considerable deviations in the stability properties from the third-order analysis and gives better results consistent with the exact numerical results. Furthermore, the influence of linear shear current on Peregrine breather (PB) is studied.
SponsorThis work was started during a visit by Professor A. K. Dhar to the University of Delaware. Professor J.T. Kirby was supported by the National Science Foundation, Physical Oceanography Program under Grant No. OCE-1756355. Professor A. K. Dhar wishes to acknowledge and sincerely thank the Indian Institute of Engineering Science and Technology, Shibpur for providing him the financial support through CPDA under Grant No. RDO/453/18. We thank the referees for their suggestions for improving the manuscript.
CitationA. K. Dhar and James T. Kirby , "Fourth-order stability analysis for capillary-gravity waves on finite-depth currents with constant vorticity", Physics of Fluids 35, 026601 (2023) https://doi.org/10.1063/5.0136002
ISSN1089-7666
URLhttps://udspace.udel.edu/handle/19716/32620
Languageen_US
PublisherPhysics of Fluids
TitleFourth-order stability analysis for capillary-gravity waves on finite-depth currents with constant vorticity
TypeArticle
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