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Reynolds stress and eddy viscosity in direct numerical simulations of sheared two-dimensional turbulence

Published online by Cambridge University Press:  10 June 2010

PATRICK F. CUMMINS  and
GREG HOLLOWAY
PATRICK F. CUMMINS*
Affiliation:
Institute of Ocean Sciences, Fisheries and Oceans Canada, 9860 W. Saanich Road, Sidney, BC, CanadaV8L 4B2
GREG HOLLOWAY
Affiliation:
Institute of Ocean Sciences, Fisheries and Oceans Canada, 9860 W. Saanich Road, Sidney, BC, CanadaV8L 4B2
*
†Email address for correspondence: [email protected]
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Abstract

The Reynolds stress associated with the adjustment of two-dimensional isotropic eddies subject to a large-scale shear flow is examined in a series of initial-value calculations in a periodic channel. Several stages in the temporal evolution of the stress can be identified. Initially, there is a brief period associated with quasi-passive straining of the eddy field in which the net Reynolds stress and the associated eddy viscosity remain essentially zero. In spectral space this is characterized by mutual cancellation of contributions to the Reynolds stress at high and low eddy wavenumbers. Subsequently, eddy–eddy interactions produce a tendency to restore isotropy at higher eddy wavenumbers, leading to an overall positive eddy viscosity associated with the dominant contribution to the Reynolds stress at low eddy wavenumbers. These results are consistent with theoretical predictions of positive eddy viscosity for initially isotropic homogeneous two-dimensional turbulence. Due to the inverse cascade, the accumulation with time of energy at the scale of the channel produces a competing tendency to negative eddy viscosity associated with linear shearing of the disturbances. This finite-domain effect may become dominant if the nonlinearity of the eddy field is relatively weak.

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Papers
Information
Journal of Fluid Mechanics , Volume 657 , 25 August 2010 , pp. 394 - 412
Copyright
Copyright © Cambridge University Press 2010

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