Transversally periodic solitary gravity-capillary waves

Paul A. Milewski, Zhan Wang

Research output: Contribution to journalArticle

8 Citations (Scopus)
131 Downloads (Pure)

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 languageEnglish
Article number20130537
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Volume470
Issue number2161
Early online date30 Oct 2013
DOIs
Publication statusPublished - Jan 2014

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