TY - JOUR
T1 - Hydroelastic solitary waves in deep water
AU - Milewski, Paul A.
AU - Vanden-Broeck, J. M.
AU - Wang, Zhan
N1 - Funding Information:
This work was supported by the EPSRC under grant GR/S47786/01 and by the Division of Mathematical Sciences of the National Science Foundation under grant NSF-DMS-0908077.
PY - 2011/7/25
Y1 - 2011/7/25
N2 - 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.
AB - 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.
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U2 - 10.1017/jfm.2011.163
DO - 10.1017/jfm.2011.163
M3 - Article
AN - SCOPUS:80052168155
SN - 0022-1120
VL - 679
SP - 628
EP - 640
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -