Abstract
The joint effects of weak nonlinearity and weak linear damping on the dominant, antisymmetric gravity wave (excited by torsional oscillations of a plane wavemaker about a vertical axis) near its cutoff frequency in a rectangular channel are investigated, following Barnard, Mahony & Pritchard (1977). The evolution equations for the envelope of this mode are derived from the variational formulation previously developed for the parametrically excited cross-wave problem (Miles & Becker 1988). They are equivalent to those of Barnard et al., after correcting their damping and self-interaction terms, and, after appropriate normalization, differ from the cross-wave evolution equations only in the boundary condition at the wavemaker. Analytical approximations and the results of numerical integration for stationary envelopes (as observed in the experiments of Barnard et al.) are presented. The present results are somewhat closer to the observations of Barnard et al. than are their calculations, but the differences between the two calculations are not qualitatively significant.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
