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Two-dimensional flows with zero net momentum: evolution of vortex quadrupoles and oscillating-grid turbulence

Published online by Cambridge University Press:  26 April 2006

S. I. Voropayev ,
Y. D. Afanasyev  and
G. J. F. van Heijst
S. I. Voropayev
Affiliation:
Institute of Oceanology, Russian Academy of Sciences, Krasikova 23, Moscow 117851, Russia
Y. D. Afanasyev
Affiliation:
Institute of Oceanology, Russian Academy of Sciences, Krasikova 23, Moscow 117851, Russia
G. J. F. van Heijst
Affiliation:
J. M. Burgers Centre for Fluid Mechanics, Department of Technical Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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Abstract

The planar flow arising in an initially quiescent viscous fluid under the action of a localized dipolar-type forcing has been studied analytically and experimentally. The force dipole, with non-dimensional forcing amplitude Re, brings net zero momentum into the fluid and gives rise to the formation of a quadrupolar vortex: a system of two dipolar vortices moving apart. Experimentally, the action of a force dipole was modelled by a vertical cylinder oscillating horizontally in the shallow upper layer of a two-layer fluid. Two cases were studied: single quadrupoles and an array of quadrupoles. It is found that single quadrupoles develop in a self-similar manner: the length L and the translation velocity Ū of the quadrupolar vortex change with time as L ∼ t1/2 and Ū ∼ t-1/2. These quantities are characterized by non-dimensional functions α(Re) and β(Re), respectively, which have been determined theoretically for small Re-values and experimentally for Re-values in the range 160–2200.

To produce an array of quadrupoles an array of oscillating vertical rods was used. Two stages in the flow evolution were studied experimentally: the initial stage, when the interactions between the quadrupoles are weak, and the intermediate stage when the interactions play an essential role and the flow is (two-dimensionally) turbulent. It is found that at both stages the width H of the region with intense vortical motions increases with time as H ∼ t1/2. A theoretical explanation of the experimental results is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 282 , 10 January 1995 , pp. 21 - 44
Copyright
© 1995 Cambridge University Press

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