Milewski, P. A., Vanden-Broeck, J.-M. and Wang, Z., 2011. Hydroelastic solitary waves in deep water. Journal of Fluid Mechanics, 679, pp. 628-640.
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.
|Item Type ||Articles|
|Creators||Milewski, P. A., Vanden-Broeck, J.-M. and Wang, Z.|
|Departments||Faculty of Science > Mathematical Sciences|
|Research Centres||EPSRC Centre for Doctoral Training in Statistical Mathematics (SAMBa)|
|Publisher Statement||S0022112011001637a.pdf: © Cambridge University Press|
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