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Scaling of decaying shallow axisymmetric swirl flows

Published online by Cambridge University Press:  07 April 2010

M. DURAN-MATUTE ,
L. P. J. KAMP ,
R. R. TRIELING  and
G. J. F. van HEIJST
M. DURAN-MATUTE*
Affiliation:
Department of Applied Physics and J. M. Burgers Centre, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
L. P. J. KAMP
Affiliation:
Department of Applied Physics and J. M. Burgers Centre, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
R. R. TRIELING
Affiliation:
Department of Applied Physics and J. M. Burgers Centre, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
G. J. F. van HEIJST
Affiliation:
Department of Applied Physics and J. M. Burgers Centre, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
*
†Email address for correspondence: m.duran.matute@tue.nl
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Abstract

There is a lack of rigour in the usual explanation for the scaling of the vertical velocity of shallow flows based on geometrical arguments and the continuity equation. In this paper we show, by studying shallow axisymmetric swirl flows, that the dynamics of the flow are crucial to determine the proper scaling. In addition, we present two characteristic scaling parameters for such flows: Reδ2 for the radial velocity and Reδ3 for the vertical velocity, where Re is the Reynolds number of the swirl flow and δ=H/L is the flow aspect ratio with H the fluid depth and L a typical horizontal length scale. This scaling contradicts the common assumption that the vertical velocity should scale with the primary motion proportional to the aspect ratio δ. Moreover, if this scaling applies, then the primary flow can be considered as quasi-two-dimensional. Numerical simulations of a decaying Lamb–Oseen vortex served to test the analytical results and to determine their range of validity. It was found that the primary flow can be considered as quasi-two-dimensional only if δRe1/2≲3 and δRe1/3≲1.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 471 - 484
Copyright
Copyright © Cambridge University Press 2010

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