Instability of capillary-gravity waves in water of arbitrary uniform depth
The Benjamin-Feir instability [\textit{T. B. Benjamin} and \textit{J. Feir}, J. Fluid Mech. 27, 417-430 (1967; Zbl 0144.471)] of periodic capillary- gravity waves on a liquid layer of arbitrary uniform depth is investigated. When surface tension is present, there is always instability for some wavenumber and liquid depth and bounds on the sideband frequencies for unbounded amplification are derived. The results are compared with the slow modulation theory using an averaged Lagrangian.
scientific article; zbMATH DE number 4022885