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Scaling laws for homogeneous turbulent shear flows in a rotating frameThe scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri = -2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.
Document ID
19890042317
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Speziale, Charles G.
(NASA Langley Research Center Hampton, VA, United States)
Mhuiris, Nessan Macgiolla
(NASA Langley Research Center; Institute for Computer Applications in Science and Engineering Hampton, VA, United States)
Date Acquired
August 14, 2013
Publication Date
February 1, 1989
Publication Information
Publication: Physics of Fluids A
Volume: 1
ISSN: 0899-8213
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
89A29688
Funding Number(s)
CONTRACT_GRANT: NAS1-18107
Distribution Limits
Public
Copyright
Other

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