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Particle transport in a random velocity field with Lagrangian statistics | | Piero Olla
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3 Dec 2001 | | Subject: | Chaotic Dynamics | nlin.CD | | Affiliation: | ISAC-CNR, Universita’ di 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 regime, are analyzed. The concentration spectrum is predicted to obey, above the scale of eddies with lifetime equal to the Stokes time, a power law with universal -4/3 exponent, and to be otherwise independent of the nature of the turbulent flow. A preference of the solid particle to lie in less energetic regions of the flow is observed. | | Source: | arXiv, nlin.CD/0201003 | | Other source: | [GID 376672] pmid12513593 | | Services: | Forum | Review | PDF | Favorites | |
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