Stochastic suspensions of heavy particles

PHYSICA D-NONLINEAR PHENOMENA

卷:237

Article

Bec, Jeremie¹  Cencini, Massimo^2,3  Hillerbrand, Rafaela⁴  Turitsyn, Konstantin^5,6 

[1] Univ Nice, CNRS, Observ Cote Azur, Lab Cassiopee, Bd Observ, F-06300 Nice, France

[2] Univ Roma La Sapienza, Dip Fis, SMC INFM CNR, I-00185 Rome, Italy

[3] Ist Sistemi Complessi, CNR, I-00185 Rome, Italy

[4] Univ Oxford, Future Human Inst, Oxford OX1 1PT, England

[5] Univ Chicago, James Franck Inst, Chicago, IL 60637 USA

[6] LD Landau Theoret Phys Inst, Moscow 119334, Russia

关键词: stochastic flows;    inertial particles;    Kraichnan model;    Lyapunov exponent;   

DOI  :  10.1016/j.physd.2008.02.022

来源: Elsevier

【 摘 要 】

Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamic and statistical properties. Substantial progress followed from the study of suspensions in model flows which, although much simpler, reproduce most of the important mechanisms observed in real turbulence. This paper presents recent developments made on the relative motion of a pair of particles suspended in time-uncorrelated and spatially self-similar Gaussian flows. This review is complemented by new results. By introducing a time-dependent Stokes number, it is demonstrated that inertial particle relative dispersion recovers asymptotically Richardson's diffusion associated to simple tracers. A perturbative (homogeneization) technique is used in the small-Stokes-number asymptotics and leads to interpreting first-order corrections to tracer dynamics in terms of an effective drift. This expansion implies that the correlation dimension deficit behaves linearly as a function of the Stokes number. The validity and the accuracy of this prediction is confirmed by numerical simulations. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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