Geometric properties of particle trajectories in turbulent flows

Abstract

We study the statistics of curvature and torsion of Lagrangian trajectories from direct numerical simulations of homogeneous and isotropic turbulence (at e _λ ≈280) in order to extract informations on the geometry of small-scale coherent structures in turbulent flows. We find that, as previously observed by Braun et al. (W. Braun, F. De Lillo, and B. Eckhardt, Geometry of particle paths in turbulent flows, J. Turbul. 7 (2006), p. 62) and Xu et al. (H. Xu, N.T. Ouellette, and E. Bodenschatz, Curvature of Lagrangian trajectories in turbulence, Phys. Rev. Lett. 98 (2007), p. 050201), the high curvature statistics is dominated by large-scale flow reversals where velocity magnitude assumes very low values. We show that flow-reversal events are characterized by very short correlation times. We introduce both time filtering and threshold in the minimum velocity amplitude in order to disentangle intense curvature events generated from genuine small-scale vortex structures from simple flow-reversal. We present for the first time measurements of torsion statistics in fully developed turbulent flows. By studying the joint statistics of curvature and torsion, we present further evidences that intense and persistent events are dominated by helical-type trajectories.

Keywords:

• Lagrangian turbulence
• chaotic advection
• differential geometry

Acknowledgements

I gratefully thank L. Biferale for his precious suggestions and one of the referees of the manuscript who contributed to greatly improve the quality of the paper with his/her remarks during the review process. I would also like to acknowledge useful and interesting discussions with F. Toschi and A. S. Lanotte.