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Guided surface waves near cutoff

Published online by Cambridge University Press:  21 April 2006

John Miles
John Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, CA 92093, USA
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 189 , April 1988 , pp. 287 - 300
Copyright
© 1988 Cambridge University Press

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