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Nonlinear hydroelastic waves on a linear shear current at finite depth

Nonlinear hydroelastic waves on a linear shear current at finite depth

Gao, T. ORCID: 0000-0002-6425-1568, Wang, Z. and Milewski, P. A. (2019) Nonlinear hydroelastic waves on a linear shear current at finite depth. Journal of Fluid Mechanics, 876. pp. 55-86. ISSN 0022-1120 (Print), 1469-7645 (Online) (doi:https://doi.org/10.1017/jfm.2019.528)

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Abstract

This work is concerned with waves propagating on water of finite depth with a constant-vorticity current under a deformable flexible sheet. The pressure exerted by the sheet is modelled by using the Cosserat thin shell theory. By means of multi-scale analysis, small amplitude nonlinear modulation equations in several regimes are considered, including the nonlinear Schrödinger equation (NLS) which is used to predict the existence of small-amplitude wavepacket solitary waves in the full Euler equations and to study the modulational instability of quasi-monochromatic wavetrains. Guided by these weakly nonlinear results, fully nonlinear steady and time-dependent computations are performed by employing a conformal mapping technique. Bifurcation mechanisms and typical profiles of solitary waves for different underlying shear currents are presented in detail. It is shown that even when small-amplitude solitary waves are not predicted by the weakly nonlinear theory, we can numerically find large-amplitude solitary waves in the fully nonlinear equations. Time-dependent simulations are carried out to confirm the modulational stability results and illustrate possible outcomes of the nonlinear evolution in unstable cases.

Item Type: Article
Uncontrolled Keywords: hydroelastic waves, solitary waves, modulational instabilities
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Liberal Arts & Sciences
Faculty of Liberal Arts & Sciences > Department of Mathematical Sciences
Last Modified: 31 Jan 2020 01:38
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/25949

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