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)
|
PDF (Author's Accepted Manuscript)
25949 GAO_Nonlinear_Hydroelastic_Waves_On_A_Linear_Shear_Current_At_Finite_Depth_(AAM)_2019.pdf - Accepted Version Download (1MB) | Preview |
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 |
Actions (login required)
View Item |
Downloads
Downloads per month over past year