Gao, T. ORCID: https://orcid.org/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: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 / School / Research Centre / Research Group:	Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS) Faculty of Engineering & Science
Last Modified:	04 Mar 2022 13:06
URI:	http://gala.gre.ac.uk/id/eprint/25949

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