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Investigation of symmetry breaking in periodic gravity-capillary waves

Investigation of symmetry breaking in periodic gravity-capillary waves

Gao, T. ORCID: 0000-0002-6425-1568, Wang, Z. and Vanden-Broeck, J.-M. (2016) Investigation of symmetry breaking in periodic gravity-capillary waves. Journal of Fluid Mechanics, 811. pp. 622-641. ISSN 0022-1120 (Print), 1469-7645 (Online) (doi:https://doi.org/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.

Item Type: Article
Uncontrolled Keywords: capillary-gravity waves, non-symmtric waves
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Liberal Arts & Sciences
Faculty of Liberal Arts & Sciences > Department of Mathematical Sciences
Last Modified: 13 Dec 2019 12:59
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/25955

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