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Structure of a steady drain-hole vortex in a viscous fluid

Published online by Cambridge University Press:  10 June 2010

L. BØHLING ,
A. ANDERSEN  and
D. FABRE
L. BØHLING
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
A. ANDERSEN*
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
D. FABRE
Affiliation:
Université de Toulouse, INPT, UPS; Institut de Mécanique des Fluides de Toulouse (IMFT), Allée du Professeur Camille Soula, F-31400, Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

We use direct numerical simulations to study a steady bathtub vortex in a cylindrical tank with a central drain-hole, a flat stress-free surface and velocity prescribed at the inlet. We find that the qualitative structure of the meridional flow does not depend on the radial Reynolds number, whereas we observe a weak overall rotation at a low radial Reynolds number and a concentrated vortex above the drain-hole at a high radial Reynolds number. We introduce a simple analytically integrable model that shows the same qualitative dependence on the radial Reynolds number as the simulations and compares favourably with the results for the radial velocity and the azimuthal velocity at the surface. Finally, we describe the height dependence of the radius of the vortex core and the maximum of the azimuthal velocity at a high radial Reynolds number, and we show that the data on the radius of the vortex core and the maximum of the azimuthal velocity as functions of height collapse on single curves by appropriate scaling.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 656 , 10 August 2010 , pp. 177 - 188
Copyright
Copyright © Cambridge University Press 2010

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