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On the effect of the molecular diffusivity in turbulent diffusion

Published online by Cambridge University Press:  28 March 2006

P. G. Saffman
P. G. Saffman
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

It is shown that the dispersion of a substance, with molecular diffusivity κ, in a stationary, homogeneous, turbulent velocity field can be formulated in terms of a ‘substance auto-correlation function’, this being a generalization of the well-known Lagrangian correlation between the velocity of a fluid particle at different times. It is found that the interaction between the molecular diffusion and the turbulent motion reduces the dispersion from the value it would have if the processes of molecular and turbulent diffusion were independent and additive. The conflict, between the results obtained in this paper and previous results which implied that the interaction increases the dispersion, is resolved. The ratio, of the contributions to the dispersion from the interaction term and the turbulent diffusion term, is obtained for comparatively large times by the use of intuitive arguments, and is found to be inversely proportional to the Prandtl number and a Reynolds number of the turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 8 , Issue 2 , June 1960 , pp. 273 - 283
Copyright
© 1960 Cambridge University Press

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References

Batchelor, G. K. & Townsend, A. A. 1956 Article in Surveys in Mechanics, p. 352. Cambridge University Press.
Mickelsen, W. R. 1960 J. Fluid Mech. 7, 397.
Taylor, G. I. 1921 Proc. Lond. Math. Soc. 20, 196.
Townsend, A. A. 1951 Proc. Roy. Soc. A, 209, 418.
Townsend, A. A. 1954 Proc. Roy. Soc. A, 224, 487.