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On higher order Bragg resonance of water waves by bottom corrugations

Published online by Cambridge University Press:  12 July 2010

JIE YU  and
LOUIS N. HOWARD
JIE YU*
Affiliation:
Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC 27695-7908, USA
LOUIS N. HOWARD
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

The exact theory of linearized water waves in a channel of indefinite length with bottom corrugations of finite amplitude (Howard & Yu, J. Fluid Mech., vol. 593, 2007, pp. 209–234) is extended to study the higher order Bragg resonances of water waves occurring when the corrugation wavelength is close to an integer multiple of half a water wavelength. The resonance tongues (ranges of water-wave frequencies) are given for these higher order cases. Within a resonance tongue, the wave amplitude exhibits slow exponential modulation over the corrugations, and slow sinusoidal modulation occurs outside it. The spatial rate of wave amplitude modulation is analysed, showing its quantitative dependence on the corrugation height, water-wave frequency and water depth. The effects of these higher order Bragg resonances are illustrated using the normal modes of a rectangular tank.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 659 , 25 September 2010 , pp. 484 - 504
Copyright
Copyright © Cambridge University Press 2010

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