Guided Surface Waves Near Cutoff

摘要

The joints 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. The evolution equations for the envelope of this mode are derived from the variational formulation previously developed for the parametrically excited cross-wave problem. They are equivalent to those of the first study 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 are presented. The present results are somewhat closer to the observations of the first study than are their calculations, but the differences between the two calculations are not qualitatively significant. Keywords: Nonlinear waves, Wave tanks, Surface waves, Reprints. (jdh)