Faraday resonance in two-dimensional standing gravity waves of finite depth

Citation
Y. Wada et M. Okamura, Faraday resonance in two-dimensional standing gravity waves of finite depth, WAVE MOTION, 35(2), 2002, pp. 125-140
Citations number
6
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics,"Optics & Acoustics
Journal title
WAVE MOTION
ISSN journal
0165-2125 → ACNP
Volume
35
Issue
2
Year of publication
2002
Pages
125 - 140
Database
ISI
SICI code
0165-2125(200202)35:2<125:FRITSG>2.0.ZU;2-0
Abstract
Faraday waves arise on the surface of a liquid in a container that is under going vertical periodic oscillations. The motion of two resonant modes with natural frequencies in the approximate ratio 3:1 is considered in this pap er. We derive the nonlinear evolution equations of the dominant free-surfac e modes up to fifth-order in wave amplitude. It is found that the third-ord er evolution equations are integrable while the fifth-order evolution equat ions are chaotic, which shows that the fifth-order nonlinearity breaks the integrability of the third-order integrable system. (C) 2002 Elsevier Scien ce B.V. All rights reserved.