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The effective long-time diffusivity for a passive scalar in a Gaussian model fluid flow

Published online by Cambridge University Press:  19 April 2006

R. Phythian and
W. D. Curtis
R. Phythian
Affiliation:
Department of Physics, University College of Swansea, Wales
W. D. Curtis
Affiliation:
Department of Physics, University College of Swansea, Wales
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Abstract

The problem considered is the diffusion of a passive scalar in a ‘fluid’ in random motion when the fluid velocity field is Gaussian and statistically homogeneous, isotropic and stationary. A self-consistent expansion for the effective long-time diffusivity is obtained and the approximations derived from this series by retaining up to three terms are explicitly calculated for simple idealized forms of the velocity correlation function for which numerical simulations are available for comparison for zero molecular diffusivity. The dependence of the effective diffusivity on the molecular diffusivity is determined within this idealization. The results support Saffman's contention that the molecular and turbulent diffusion processes interfere destructively, in the sense that the total effective diffusivity about a fixed point is less than that which would be obtained if the two diffusion processes acted independently.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 2 , 28 November 1978, pp. 241 - 250
Copyright
© 1978 Cambridge University Press

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