Velocity gradients along particles trajectories in turbulent flows.pdf

a r X i v : 0 8 0 6 .4 7 6 2 v 1 [ p h y s i c s .f l u - d y n ] 3 0 J u n 2 0 0 8 Velocity gradients along particles trajectories in turbulent flows Roberto Benzi,1 Luca Biferale,1 Enrico Calzavarini,2, 3 Detlef Lohse,2 and Federico Toschi4 1Dept Physics and INFN, University of Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy 2Department of Applied Physics, University of Twente, 7500 AE Enschede, The Netherlands. 3Lab. de Physique, E?cole Normale Supe?rieure de Lyon, CNRS UMR5672, 46 Alle?e d’ Italie, 69007 Lyon, France. 4CNR-IAC, Viale del Policlinico 137, 00161 Roma, Italy, and INFN, Sezione di Ferrara, Via G. Saragat 1, 44100 Ferrara, Italy. (Dated: June 30, 2008) We present an investigation of the statistics of velocity gradients along the trajectories of neutral tracers and of heavy/light particles advected by an homogeneous and isotropic turbulent flow. We propose a Lagrangian rephrasing of the Refined Kolmogorov Similarity Hypothesis (RKSH) and test its validity along the particle trajectories. We perform our study on state-of-the-art numerical data coming from numerical simulations up to Reλ ～ 400 with 2048 3 collocation points. We show that the Lagrangian RKSH is well verified for time lags larger than the typical response time of the particle, τp. Implication of these findings for modeling of particle transport in many applied problems are also discussed. PACS numbers: 47.27.-i, 47.10.-g One of the most prominent feature of turbulent flows are the strong variations in the energy dissipation field, a phenomenon called intermittency [1]. In an attempt to describe quantitatively intermittent fluctuations, Kol- mogorov and Oboukhov in 1962 [2] proposed a general re- lation linking velocity fluctuations, measured at a given spatial increment δru = u(x + r, t) ? u(x, t), with the statistical properties of the coarse grained energy dissi- pation, εr = r ?3 ∫ Λ(r) ε(x) d3x averaged over a volume, Λ(r), of typical linear size r: δru ～ r 1/3