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Particle transport in a random velocity

field with Lagrangian statistics

Piero Olla

ISAC-CNR

Sezione di Lecce

73100 Lecce Italy

**Abstract**

The transport properties of a random velocity field with Kolmogorov spectrum and time correlations defined along Lagrangian trajectories are analyzed. The analysis is carried on in the limit of short correlation times, as a perturbation theory in the ratio, scale by scale, of the eddy decay and turn-over time. Various quantities such as the Batchelor constant and the dimensionless constants entering the expression for particle relative and self-diffusion are given in terms of this ratio and of the Kolmogorov constant. Particular attention is paid to particles with finite inertia. The self-diffusion properties of a particle with Stokes time longer than the Kolmogorov time are determined, verifying on an analytical example the dimensional results of $[$nlin.CD/0103018$]$. Expressions for the fluid velocity Lagrangian correlations and correlation times along a solid particle trajectory, are provided in several parameter regimes, including the infinite Stokes time limit corresponding to Eulerian correlations. The concentration fluctuation spectrum and the non-ergodic properties of a suspension of heavy particles in a turbulent flow, in the same 