Projects per year
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.
|Journal||Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences|
|Early online date||30 Oct 2013|
|Publication status||Published - Jan 2014|
FingerprintDive into the research topics of 'Transversally periodic solitary gravity-capillary waves'. Together they form a unique fingerprint.
- 1 Finished
12/11/12 → 11/11/15
Project: Research council