Gao, T;
Wang, Z;
Vanden-Broeck, J-M;
(2017)
Investigation of symmetry breaking in periodic gravity–capillary waves.
Journal of Fluid Mechanics
, 811
pp. 622-641.
10.1017/jfm.2016.751.
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Abstract
In this paper, fully nonlinear non-symmetric periodic gravity–capillary waves propagating at the surface of an inviscid and incompressible fluid are investigated. This problem was pioneered analytically by Zufiria (J. Fluid Mech., vol. 184, 1987c, pp. 183–206) and numerically by Shimizu & Shōji (Japan J. Ind. Appl. Maths, vol. 29 (2), 2012, pp. 331–353). We use a numerical method based on conformal mapping and series truncation to search for new solutions other than those shown in Zufiria (1987c) and Shimizu & Shōji (2012). It is found that, in the case of infinite-depth, non-symmetric waves with two to seven peaks within one wavelength exist and they all appear via symmetry-breaking bifurcations. Fully exploring these waves by changing the parameters yields the discovery of new types of non-symmetric solutions which form isolated branches without symmetry-breaking points. The existence of non-symmetric waves in water of finite depth is also confirmed, by using the value of the streamfunction at the bottom as the continuation parameter.
| Type: | Article |
|---|---|
| Title: | Investigation of symmetry breaking in periodic gravity–capillary waves |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/jfm.2016.751 |
| Publisher version: | https://doi.org/10.1017/jfm.2016.751 |
| Language: | English |
| Additional information: | This article has been published in a revised form in Journal of Fluid Mechanics [http://dx.doi.org/10.1017/jfm.2016.751.] This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press 2016. |
| Keywords: | Capillary waves, surface gravity waves, waves/free-surface flows |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1542961 |
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