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Turbulent pair dispersion and scalar diffusion

Published online by Cambridge University Press:  20 April 2006

T. S. Lundgren
T. S. Lundgren
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307 Permanent address: Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455.
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Abstract

A method of treating turbulent pair dispersion and scalar diffusion is presented. Use is made of Kraichnan's form of Richardson's diffusion equation by relating the turbulent pair diffusivity to single-time Eulerian velocity statistics (which are presumed known) by means of a statistical independence hypothesis. In this procedure the diffusivity itself is coupled to solutions of the diffusivity equation in a self-consistent way.

The method is applied to both two-and three-dimensional flow. In three-dimensional inertial-range and dissipative-range turbulence the turbulent pair diffusivity is determined and used to find the values of the coefficients of the scalar spectrum in the $k^{-\frac{5}{3}}$ and k−1 ranges with good agreement with experiment. The Obukhov–Corrsin constant is found to be 0·49 and the Batchelor constant is √5. In two-dimensional turbulence the results are compared with constant-pressure balloon dispersion experiments. Results are also found for the rate of decay of scalar intensity in the special case where the initial scalar spectrum peaks in the inertial range.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 111 , October 1981 , pp. 27 - 57
Copyright
© 1981 Cambridge University Press

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