On the stability of weakly-nonlinear gravity-capillary waves
type: Item
instance of: scholarly article
title: On the stability of weakly-nonlinear gravity-capillary waves
zbMATH Open document ID: 0625.76049
DOI: 10.1016/0165-2125(86)90029-6
author: Jun Zhang
author: W. Kendall Melville
published in: Wave Motion
publication date: 1986-01-01T00:00:00Z
review text: A coupled set of equations, initially derived by \textit{D. J. Benney} [Stud. Appl. Math. 55, 93-106 (1976; Zbl 0352.76017)], is used to study the linear stability of weakly-nonlinear gravity-capillary waves to resonant triad and quartet interactions in two dimensions. The eigenvalue system is discussed for each class of resonances and certain subtleties regarding Hasselman's criterion and long wave-short wave resonances are resolved. The eigenvalue system is solved numerically and it is shown that the triad and quartet instabilities that are separated in wavenumber space for infinitesimal waves may merge for weakly nonlinear waves.
Mathematics Subject Classification ID: 76E17
Mathematics Subject Classification ID: 76E99
Mathematics Subject Classification ID: 76B45
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4016457
zbMATH Keywords: unstable modes
zbMATH Keywords: two-dimensional gravity-wave trains
zbMATH Keywords: deep-water gravity- capillary waves
zbMATH Keywords: linear stability
zbMATH Keywords: weakly-nonlinear gravity-capillary waves
zbMATH Keywords: quartet interactions
zbMATH Keywords: eigenvalue system
MaRDI profile type: Publication
full work available at URL: 0165-2125(86)90029-6
OpenAlex ID: W2146404577
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description: scientific article; zbMATH DE number 4016457