Hydroelastic solitary waves in deep water

Paul A. Milewski, J-M. Vanden-Broeck, Zhan Wang

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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.
Original languageEnglish
Pages (from-to)628-640
Number of pages13
JournalJournal of Fluid Mechanics
Volume679
Early online date18 May 2011
DOIs
Publication statusPublished - Jul 2011

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deep water
Solitons
solitary waves
Water
elastic sheets
ideal fluids
asymptotic methods
Ice
Numerical methods
ice
Fluids

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Hydroelastic solitary waves in deep water. / Milewski, Paul A.; Vanden-Broeck, J-M.; Wang, Zhan.

In: Journal of Fluid Mechanics, Vol. 679, 07.2011, p. 628-640.

Research output: Contribution to journalArticle

Milewski, Paul A. ; Vanden-Broeck, J-M. ; Wang, Zhan. / Hydroelastic solitary waves in deep water. In: Journal of Fluid Mechanics. 2011 ; Vol. 679. pp. 628-640.
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