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On gravity-wave scattering by non-secular changes in depth

Published online by Cambridge University Press:  10 December 1998

JOHN MILES
Affiliation:
Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, CA 92093-0225, USA

Abstract

The reflection of a straight-crested gravity wave by a non-secular perturbation h1(x) in depth relative to an otherwise flat bottom of depth h0 is calculated through an expansion in ε∝h1/h0. Explicit results are developed up to second order for the sinusoidal patch h1=−bsin(mπx/l), 0<x<l, and reduced for Bragg resonance. Trapped modes are absent at first order but appear at second order and contribute O2)/O3) to the maximum (Bragg-resonant) reflection coefficient for odd/even m. A third-order approximation that includes the dominant contributions of the third-order components of the resonant peak of the reflection coefficient for large m, but neglects the trapped modes, predicts resonant peaks that agree with the values measured by Davies & Heathershaw (1984).

Type
Research Article
Copyright
© 1998 Cambridge University Press

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