On the stability of weakly-nonlinear gravity-capillary waves
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.
weakly-nonlinear gravity-capillary waves
scientific article; zbMATH DE number 4016457