Abstract
| Language | English |
|---|---|
| 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 | |
| Status | Published - Jan 2014 |
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Transversally periodic solitary gravity-capillary waves. / Milewski, Paul A.; Wang, Zhan.
In: Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, Vol. 470, No. 2161, 20130537, 01.2014.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Transversally periodic solitary gravity-capillary waves
AU - Milewski, Paul A.
AU - Wang, Zhan
PY - 2014/1
Y1 - 2014/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84890102568&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1098/rspa.2013.0537
U2 - 10.1098/rspa.2013.0537
DO - 10.1098/rspa.2013.0537
M3 - Article
VL - 470
JO - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
T2 - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
SN - 1364-503X
IS - 2161
M1 - 20130537
ER -