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Nonlinear resonant oscillations in open tubes

Published online by Cambridge University Press:  29 March 2006

Brian R. Seymour  and
Michael P. Mortell
Brian R. Seymour
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver
Michael P. Mortell
Affiliation:
Department of Mathematical Physics, University College, Cork, Ireland
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Abstract

A gas in a tube, one end of which is open, is driven by a periodic applied velocity or pressure at or near a resonant frequency. Damping is introduced into the system by radiation of energy through the open end. It is shown that shocks are possible at an open end and that there is a critical level of damping which ensures a continuous gas response for all frequencies. At the critical level the amplitude of the response is O(ε1/3), where ε is the amplitude of the input, and it is bounded by the amplitude predicted by linear theory. There is agreement with the qualitative experimental results available.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 4 , 9 October 1973 , pp. 733 - 749
Copyright
© 1973 Cambridge University Press

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