UNSPECIFIED (1992) UNIFORMLY TRAVELING WATER-WAVES FROM A DYNAMIC-SYSTEMS VIEWPOINT - SOME INSIGHTS INTO BIFURCATIONS FROM STOKES FAMILY. JOURNAL OF FLUID MECHANICS, 241 . pp. 333-347. ISSN 0022-1120

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Abstract

Numerical work of many people on the bifurcations of uniformly travelling water waves (two-dimensional irrotational gravity waves on inviscid fluid of infinite depth) suggests that uniformly travelling water waves have a reversible Hamiltonian formulation, where the role of time is played by horizontal position in the wave frame. ln this paper such a formulation is presented. Based on this viewpoint, some insights are given into bifurcations from Stokes' family of periodic waves. It is demonstrated numerically that there is a 'fold point' at amplitude A0 almost-equal-to 0.40222. Assuming non-degeneracy of the fold and existence of an associated centre manifold, this explains why a sequence of p/q-bifurcations occurs on one side of A0, with 0 < p/q less-than-or-equal-to 1/2, in the order of the rationals. Secondly, it explains why no symmetry-breaking bifurcation is observed at A0, contrary to the expectations of some. Thirdly, it explains why the bifurcation tree for periodic uniformly travelling waves looks so much like that for the area-preserving Henon map. Fourthly, it leads to predictions of a rich variety of spatially quasi-periodic, heteroclinic and chaotic waves.

Item Type:	Journal Article
Subjects:	T Technology > TJ Mechanical engineering and machinery Q Science > QC Physics
Journal or Publication Title:	JOURNAL OF FLUID MECHANICS
Publisher:	CAMBRIDGE UNIV PRESS
ISSN:	0022-1120
Date:	August 1992
Volume:	241
Number of Pages:	15
Page Range:	pp. 333-347
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/21841

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