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Capillary–gravity Kelvin–Helmholtz waves close to resonance

Published online by Cambridge University Press:  26 April 2006

V. Bontozoglou  and
T. J. Hanratty
V. Bontozoglou
Affiliation:
Department of Chemical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Present address: Chemical Process Engineering Research Institute, PO Box 19517, 54006 Thessaloniki, Greece.
T. J. Hanratty
Affiliation:
Department of Chemical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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Abstract

Capillary–gravity waves of permanent form at the interface between two unbounded fluids in relative motion are considered. The range of wavelengths for an internal resonance with the second harmonic and a period-doubling bifurcation are found to depend on the current speed. The Kelvin–Helmholtz instability of short waves becomes strongly subcritical near resonance. It is speculated that this instability is needed to trigger a period-doubling bifurcation. This notion is used to explain the development of waves at short fetch and the initiation of liquid slugs for gas–liquid flow in a horizontal pipe.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 71 - 91
Copyright
© 1990 Cambridge University Press

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