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An approximate equation for the spectrum of a conserved scalar quantity in a turbulent fluid

Published online by Cambridge University Press:  28 March 2006

I. D. Howells
I. D. Howells
Affiliation:
Trinity College, Cambridge
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Abstract

The formula for transfer of $\overline {\theta^2}$-stuff across the θ-spectrum, which was obtained by Batchelor, Howells & Townsend (1959) for wave-numbers at which molecular conduction is important, is extended here to smaller wave-numbers by means of a simplified general picture of the mechanism involved. The interaction of velocity and temperature fields is represented by a combination of eddy conductivity due to the smaller eddies, and a straining action due to the larger eddies, and this leads to an approximate equation for the θ-spectrum, for a fluid of arbitrary Prandtl number, over at least the equilibrium range of wave-numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 9 , Issue 1 , September 1960 , pp. 104 - 106
Copyright
© 1960 Cambridge University Press

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References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. 1959 J. Fluid Mech. 5, 113.
Batchelor, G. K., Howells, I. D. & Townsend, A. A. 1959 J. Fluid Mech. 5, 134.