Nonlinear hydroelastic waves on a linear shear current at finite depth. (10th October 2019)

• Record Type: Journal Article
• Authors: Gao, T.; Wang, Z.; Milewski, P. A.
• Is Part Of: Journal of fluid mechanics. Volume 876(2019)
• Page Start: 55
• Page End: 86
• Publication Date: 2019-10-10
• Subjects: shear waves, -- solitary waves, -- surface gravity waves; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2019.528
• Languages: English
• ISSNs: 0022-1120

Abstract

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.