Milewski, P;
Vanden-Broeck, J-M;
Wang, Z;
(2011)
Hydroelastic solitary waves in deep water.
Journal of Fluid Mechanics
, 679
628 - 640.
10.1017/jfm.2011.163.
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Abstract
The problem of waves propagating on the surface of a two-dimensional ideal fluid of infinite depth bounded above by an elastic sheet is studied with asymptotic and numerical methods. We use a nonlinear elastic model that has been used to describe the dynamics of ice sheets. Particular attention is paid to forced and unforced dynamics of waves having near-minimum phase speed. For the unforced problem, we find that wavepacket solitary waves bifurcate from nonlinear periodic waves of minimum speed. When the problem is forced by a moving load, we find that, for small-amplitude forcing, steady responses are possible at all subcritical speeds, but for larger loads there is a transcritical range of forcing speeds for which there are no steady solutions. In unsteady computations, we find that if the problem is forced at a speed in this range, very large unsteady responses are obtained, and that when the forcing is released, a solitary wave is generated. These solitary waves appear stable, and can coexist within a sea of small-amplitude waves.
Type: | Article |
---|---|
Title: | Hydroelastic solitary waves in deep water |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1017/jfm.2011.163 |
Publisher version: | http://dx.doi.org/10.1017/jfm.2011.163 |
Language: | English |
Additional information: | © 2011 Cambridge University Press |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
URI: | https://discovery.ucl.ac.uk/id/eprint/1324413 |
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