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On the dispersion of fluid particles

Published online by Cambridge University Press:  20 April 2006

Dahe Jiang
Dahe Jiang
Affiliation:
Department of Mechanical Engineering, City College of New York, New York 10031
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Abstract

The dispersion of fluid particles in a turbulent flow is described by transition-probability density functions. A renormalized expansion is made to establish the evolution equations of these functions. The resulting equations are nonlinear integrodifferential equations written in terms of Eulerian velocity-correlation functions. For the dispersion of a single particle, the equation at the zeroth order is the same as the one obtained by Roberts (1961). For the relative dispersion of a pair of particles, the equation is more convenient for applications than those of other theories. With this equation, Richardson's $\frac{4}{3}$-power law for relative diffusion is recovered analytically based upon the Kolmogoroff spectrum and numerically based upon the von Kármán spectrum and a smoothed experimental spectrum.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 155 , June 1985 , pp. 309 - 326
Copyright
© 1985 Cambridge University Press

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