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Stability analysis and large-eddy simulation of rotating turbulence with organized eddies

Published online by Cambridge University Press:  26 April 2006

Claude Cambon ,
Jean-Pierre Benoit ,
Liang Shao  and
Laurent Jacquin
Claude Cambon
Affiliation:
Ecole Centrale de Lyon / Université Claude Bernard, Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, URA CNRS no. 263, BP 163, 69131 Ecully Cedex, France
Jean-Pierre Benoit
Affiliation:
Ecole Centrale de Lyon / Université Claude Bernard, Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, URA CNRS no. 263, BP 163, 69131 Ecully Cedex, France
Liang Shao
Affiliation:
Ecole Centrale de Lyon / Université Claude Bernard, Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, URA CNRS no. 263, BP 163, 69131 Ecully Cedex, France
Laurent Jacquin
Affiliation:
Office National d'Etudes et de Recherches Aérospatiales, BP 72, 92320 Châtillon Cedex, France
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Abstract

Rotation strongly affects the stability of turbulent flows in the presence of large eddies. In this paper, we examine the applicability of the classic Bradshaw-Richardson criterion to flows more general than a simple combination of rotation and pure shear. Two approaches are used. Firstly the linearized theory is applied to a class of rotating two-dimensional flows having arbitrary rates of strain and vorticity and streamfunctions that are quadratic. This class includes simple shear and elliptic flows as special cases. Secondly, we describe a large-eddy simulation of initially quasi-homogeneous three-dimensional turbulence superimposed on a periodic array of two-dimensional Taylor-Green vortices in a rotating frame.

The results of both approaches indicate that, for a large structure of vorticity W and subject to rotation Ω, maximum destabilization is obtained for zero tilting vorticity (½W + 2Ω = 0) whereas stability occurs for zero absolute vorticity (2Ω = 0) These results are consistent with the Bradshaw-Richardson criterion; however the numerical results show that in other cases the Bradshaw-Richardson number $B=2\Omega(W+2\Omega)/W^2$ is not always a good indicator of the flow stability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 278 , 10 November 1994 , pp. 175 - 200
Copyright
© 1994 Cambridge University Press

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