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Viscous selection of an elliptical dipole

Published online by Cambridge University Press:  20 July 2010

ZIV KIZNER ,
RUVIM KHVOLES  and
DAVID A. KESSLER
ZIV KIZNER*
Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
RUVIM KHVOLES
Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
DAVID A. KESSLER
Affiliation:
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
*
†Email address for correspondence: zinovyk@mail.biu.ac.il
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Abstract

A theory of viscous evolution and selection of symmetric two-dimensional dipoles is suggested, based on a combination of numerical simulations and an asymptotic analysis, where the slow time scale associated with the vorticity diffusion due to viscosity is incorporated. It is shown that viscosity first brings a dipole to an intermediate asymptotic state, which is independent of the initial conditions, and then slowly takes the dipole away from this state. We demonstrate that, among the variety of possible ideal-fluid dipole solutions, viscosity going to zero selects a unique solution, which is described to high accuracy by the elliptical dipole solution with a separatrix aspect ratio of 1.037.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 492 - 508
Copyright
Copyright © Cambridge University Press 2010

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References

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