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On the effect of the molecular diffusivity in turbulent diffusion

Saffman, P. G. (1960) On the effect of the molecular diffusivity in turbulent diffusion. Journal of Fluid Mechanics, 8 (2). pp. 273-283. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20181119-161052899

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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.


Item Type:Article
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https://doi.org/10.1017/s0022112060000591DOIArticle
Additional Information:© 1960 Cambridge University Press. (Received 3 October 1959) I wish to thank Dr T. H. Ellison for the benefit of a lengthy correspondence, in which a fallacy in earlier arguments, in particular the non-vanishing of the covariance (q(t) V(t + τ)), was made clear to me.
Record Number:CaltechAUTHORS:20181119-161052899
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181119-161052899
Official Citation:Saffman, P. (1960). On the effect of the molecular diffusivity in turbulent diffusion. Journal of Fluid Mechanics, 8(2), 273-283. doi:10.1017/S0022112060000591
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91049
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Nov 2018 19:36
Last Modified:20 Nov 2018 19:36

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