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CLOSURE STUDY OF THE REYNOLDS NUMBER DEPENDENCY OF THE SCALAR FLUX SPECTRUM

Wouter J. T. Bos
LMFA-CNRS Ecole Centrale de Lyon - University de Lyon 36 Avenue Guy de Collongues, 69134 Ecully Cedex, France

H. Touil
Laboratoire de Mecanique des Fluides et d'Acoustique Ecole Centrale de Lyon, France

Jean Pierre Bertoglio
Laboratoire de Mecanique des Fluides et d'Acoustique UMR 5509 Ecole Centrale de Lyon 36 Av. Guy de Collongue, 69130 Ecully, FRANCE

Аннотация

The EDQNM theory is used to study the behavior of the spectrum of the scalar flux in turbulent flow as the Reynolds number increases. In isotropic turbulence, at low and moderate Reynolds number, good agreement is observed with DNS and experimental results. The Reynolds number is varied up to a value of 107 and it is shown that at very high Reynolds numbers, the scalar flux spectrum in the inertial range behaves as predicted by the classical dimensional analysis of Lumley (1967) and scales as K−7/3. At Reynolds numbers corresponding to laboratory experiments the closure leads to a spectrum closer to K−2, showing that in the experiments the high Reynolds number asymptotic limit is not reached.
The closure is then applied to homogeneous shear flow and the spectra of cross-stream and streamwise scalar flux are investigated. The streamwise scalar flux spectrum is found to scale as K−23/9. This result is in agreement with experiments but disagrees with classical dimensional analysis. An alternative asymptotic form is proposed.