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Abstract
When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity-capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity-capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles.
Original language | English |
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Article number | 20130537 |
Journal | Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences |
Volume | 470 |
Issue number | 2161 |
Early online date | 30 Oct 2013 |
DOIs | |
Publication status | Published - Jan 2014 |
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Dive into the research topics of 'Transversally periodic solitary gravity-capillary waves'. Together they form a unique fingerprint.Projects
- 1 Finished
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Nonlinear Hydroelastic Waves with Applications to Ice Sheets
Milewski, P. (PI)
Engineering and Physical Sciences Research Council
12/11/12 → 11/11/15
Project: Research council