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Multi-mode resonances in fluids

Published online by Cambridge University Press:  26 April 2006

H. Ockendon ,
J. R. Ockendon  and
D. D. Waterhouse
H. Ockendon
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St. Giles', Oxford, OX1 3LB, UK
J. R. Ockendon
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St. Giles', Oxford, OX1 3LB, UK
D. D. Waterhouse
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St. Giles', Oxford, OX1 3LB, UK
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Abstract

When a lightly damped fluid resonator is forced near its fundamental frequency, the most usual response is one in which the fluid oscillates in the corresponding eigenmode with an amplitude response similar to that of a Duffing oscillator. Examples are the sloshing of a horizontally oscillated tank or acoustic oscillations in a resonator of general shape. However, multiple eigenmodes can be excited if the spectrum is either commensurate or degenerate and both acoustic resonance and the sloshing of shallow water in a nearly square container exemplify both these exceptional cases. In this paper we investigate how the response of such systems depends on geometry and dispersion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 315 , 25 May 1996 , pp. 317 - 344
Copyright
© 1996 Cambridge University Press

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