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Rederivation and further assessment of the LET theory of isotropic turbulence, as applied to passive scalar convection

Published online by Cambridge University Press:  26 April 2006

W. D. Mccomb ,
M. J. Filipiak  and
V. Shanmugasundaram
W. D. Mccomb
Affiliation:
Department of Physics, University of Edinburgh, King's Buildings, Mayfield Road. Edinburgh EH9 3JZ, UK
M. J. Filipiak
Affiliation:
Department of Physics, University of Edinburgh, King's Buildings, Mayfield Road. Edinburgh EH9 3JZ, UK
V. Shanmugasundaram
Affiliation:
Department of Physics, University of Edinburgh, King's Buildings, Mayfield Road. Edinburgh EH9 3JZ, UK
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Abstract

A simpler and more rigorous derivation is presented for the LET (Local Energy Transfer) theory, which generalizes the theory to the non-stationary case and which corrects some minor errors in the original formulation (McComb 1978), Previously, ad hoc generalizations of the LET theory (McComb & Shanmugasundaram 1984) gave good numerical results for the free decay of isotropic turbulence. The quantitative aspects of these previous computations are not significantly affected by the present corrections, although there are some important qualitative improvements.

The revised LET theory is also extended to the problem of passive scalar convection, and numerical results have been obtained for freely decaying isotropic turbulence, with Taylor–Reynolds numbers in the range 5 [les ] Rλ [les ] 1060, and for Prandtl numbers of 0.1, 0.5 and 1.0. At sufficiently high values of the Reynolds number, both velocity and scalar spectra are found to exhibit Kolmogorov-type power laws, with the Kolmogorov spectral constant taking the value α = 2.5 and the Corrsin–Oboukhov constant taking a value of β = 1.1.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 279 - 300
Copyright
© 1992 Cambridge University Press

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