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Experiments on standing waves in a rectangular tank with a corrugated bed

Published online by Cambridge University Press:  16 July 2015

Patrick D. Weidman ,
Andrzej Herczynski ,
Jie Yu  and
Louis N. Howard
Patrick D. Weidman*
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA
Andrzej Herczynski
Affiliation:
Department of Physics, Boston College, Chestnut Hill, MA 92467-3811, USA
Jie Yu
Affiliation:
Civil Engineering Program, Department of Mechanical Engineering, School of Marine and Atmospheric Sciences, Stony Brook University, Stony Brook, NY 11790, USA
Louis N. Howard
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: weidman@colorado.edu
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Abstract

An experimental investigation of resonant standing water waves in a rectangular tank with a corrugated bottom is reported. The study was stimulated by the theory of Howard & Yu (J. Fluid Mech., vol. 593, 2007, pp. 209–234) predicting the existence of normal modes that can be significantly affected by Bragg reflection/scattering. As a result, the amplitude of the standing waves (normal modes) varies exponentially along the entire length of the tank, or from the centre out in each direction, depending on the phase of the corrugations at the tank endwalls. Experiments were conducted in a 5 m tank fitted with a sinusoidal bottom with one adjustable endwall. Waves were excited by small-amplitude sinusoidal horizontal movement of the tank using an electrical motor drive system. Simultaneous time-series data of standing oscillations were recorded at well-separated positions along the tank to measure the growth in amplitude. Waveforms over a section of the tank were filmed through the transparent acrylic walls. Except for very shallow depths and near the tank endwalls, the experimental measurements of resonant frequencies, mean wavelengths, free-surface waveforms and amplitude growth are found in essential agreement with the Bragg resonant normal mode theory.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , pp. 122 - 150
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Copyright
© 2015 Cambridge University Press 

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