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Transient flow of a viscous incompressible fluid in a circular tube after a sudden point impulse

Published online by Cambridge University Press:  18 September 2009

B. U. FELDERHOF
B. U. FELDERHOF*
Affiliation:
Institut für Theoretische Physik A, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
*
†Email address for correspondence: ufelder@physik.rwth-aachen.de
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Abstract

The flow of a viscous incompressible fluid in a circular tube generated by a sudden impulse on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. At short time the flow is irrotational and may be described by a potential which varies with the square root of time. At later times there is a sequence of moving and decaying vortex rings. At long times the flow velocity decays with an algebraic long-time tail. The impulse generates a time-dependent pressure difference between the ends of the tube.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 637 , 25 October 2009 , pp. 285 - 303
Copyright
Copyright © Cambridge University Press 2009

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