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A comparative assessment of spectral closures as applied to passive scalar diffusion

Published online by Cambridge University Press:  20 April 2006

J. R. Herring ,
D. Schertzer ,
M. Lesieur ,
G. R. Newman ,
J. P. Chollet  and
M. Larcheveque
J. R. Herring
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307
D. Schertzer
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307 Permanent address: Direction de la Météorologie, Paris.
M. Lesieur
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307 Permanent address: Institut de Mécanique de Grenoble, Université de Grenoble.
G. R. Newman
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307 Permanent address: AVCO Systems Division, 201 Lowell Street, Wilmington, Massachusetts 01887.
J. P. Chollet
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307 Permanent address: Institut de Mécanique de Grenoble, Université de Grenoble.
M. Larcheveque
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307 Permanent address: Laboratoire de Météorologie Dynamique, Paris.
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Abstract

We compare - both analytically and numerically – two related spectral (≡ two-point) closures for the problem of the decay of temperature fluctuations convected by isotropic turbulence. The methods are the test-field model (TFM) (Kraichnan 1971; Newman & Herring 1979) and the eddy-damped quasinormal Markovian (ENQNM) approximation (Orszag 1974; Lesieur & Schertzer 1978). We show that EDQNM may be regarded as a rational approximation to, and simplification of, the TFM, except at small wavenumbers, where an additional eddy-dissipative term is needed to produce satisfactory results for the former. We consider three available methods for determining the relaxation timescales: (i) comparison with experiments, (ii) comparison with the direct-interaction approximation (DIA) in thermal equilibrium, and (iii) comparison with DIA at very small wavenumber, where it is believed to represent the dynamics properly. Comparison with both large Reynolds number and wind-tunnel Reynolds numbers is presented. For the latter, we discuss the relationship of the present theoretical results to the experiments of Warhaft & Lumley (1978) and Sreenivasan et al. (1980), and to the theoretical analysis of Corrsin (1964), Kerr & Nelkin (1980) and Antonopolos-Domis (1981).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 124 , November 1982 , pp. 411 - 437
Copyright
© 1982 Cambridge University Press

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