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Transition to turbulence in an elliptic vortex

Published online by Cambridge University Press:  26 April 2006

T. S. Lundgren  and
N. N. Mansour
T. S. Lundgren
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
N. N. Mansour
Affiliation:
NASA-Ames Research Center, Moffett Field, CA 94035, USA
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Abstract

Stability and transition to turbulence are studied in a simple incompressible two-dimensional bounded swirling flow with a rectangular planform – a vortex in a box. This flow is unstable to three-dimensional disturbances. The instability takes the form of counter-rotating swirls perpendicular to the axis which bend the vortex into a periodic wave. As these swirls grow in amplitude the primary vorticity is compressed into thin vortex layers. These develop secondary instabilities which roll up into vortex tubes. In this way the flow attains a turbulent state which is populated by intense elongated vortex tubes and weaker vortex layers which spiral around them. The flow was computed at two Reynolds numbers by spectral methods with up to 2563 resolution. At the higher Reynolds number broad three-dimensional shell-averaged energy spectra are found with nearly a decade of Kolmogorov k−5/3 law and small-scale isotropy.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 307 , 25 January 1996 , pp. 43 - 62
Copyright
© 1996 Cambridge University Press

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