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Instabilities of flow in a collapsed tube

Published online by Cambridge University Press:  26 April 2006

O. E. Jensen
O. E. Jensen
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

In a previous paper (Jensen & Pedley 1989) a model was analysed describing the effects of longitudinal wall tension and energy loss through flow separation on the existence and nature of steady flow in a finite length of externally pressurized, elastic-walled tube. The stability of these steady flows to small time-dependent perturbations is now determined. A linear analysis shows that the tube may be unstable to at least three different modes of oscillation, with frequencies in distinct bands, depending on the governing parameters; neutral stability curves for each mode are calculated. The motion of the separation point at a constriction in the tube appears to play an important role in the mechanism of these oscillations. A weakly nonlinear analysis is used to examine the instabilities in a neighbourhood of their neutral curves and to investigate mode interactions. The existence of multiple independent oscillations indicates that very complex dynamical behaviour may occur.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 220 , November 1990 , pp. 623 - 659
Copyright
© 1990 Cambridge University Press

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