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Flow-destabilized seiches in a reservoir with a movable dam

Published online by Cambridge University Press:  26 April 2011

I. J. HEWITT ,
H. SCOLAN  and
N. J. BALMFORTH
I. J. HEWITT*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada
H. SCOLAN
Affiliation:
Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), CNRS-INPG-UJF, BP 53X, 38041 Grenoble, France
N. J. BALMFORTH
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada
*
†Email address for correspondence: hewitt@math.ubc.ca
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Abstract

Using a combination of theoretical modelling and experiments, seiches in a reservoir are shown to become linearly unstable due to the coupling with flow under a dam that opens and closes in response to the upstream water pressure. The phenomenon is related to the mechanism commonly attributed to generate sound in musical instruments like the clarinet. Shallow water theory is used to model waves in the reservoir, and these are coupled, by an outflow condition, to a nonlinear oscillator equation for the dam opening. In general, several modes of oscillation are predicted to be unstable, and the frequency of the most unstable mode compares well with the dominant frequencies observed in the experiments. The experiments also show a systematic variation of the amplitude and spatial structure of the oscillations with the weight of the dam, reflecting the nonlinear coupling between the unstable modes of the system.

JFM classification

Waves/Free-surface Flows: Hydraulics Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 294 - 316
Copyright
Copyright © Cambridge University Press 2011

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