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A statistical theory of turbulent relative dispersion

Published online by Cambridge University Press:  04 January 2007

P. FRANZESE  and
M. CASSIANI
P. FRANZESE
Affiliation:
Department of Computational and Data Sciences, George Mason University, Fairfax, VA 22030, USA
M. CASSIANI
Affiliation:
Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708, USA
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Abstract

The laws governing the spread of a cluster of particles in homogeneous isotropic turbulence are derived using a theoretical approach based on inertial subrange scaling and statistical diffusion theory. The equations for the mean square dispersion of a puff admit an analytical solution in the inertial subrange and at large scales. The solution is consistent with Taylor's theory of absolute dispersion. An analytical derivation of the Richardson–Obukhov constant of relative dispersion is presented. A time scale for relative dispersion is identified, as well as relations between Lagrangian and Eulerian structure functions. The results are extended to turbulence at finite Reynolds number. A closure assumption for the relative kinetic energy, based on Taylor's theory, is presented. Comparisons with direct numerical simulations and laboratory experiments are reported.

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Papers
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Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 391 - 417
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Copyright © Cambridge University Press 2007

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