Velocity-gradient statistics along particle trajectories in turbulent flows: The refined similarity hypothesis in the Lagrangian frame

Roberto Benzi, Luca Biferale, E. Calzavarini, Detlef Lohse, F. Toschi

Research output: Contribution to journalArticleAcademicpeer-review

41 Citations (Scopus)
39 Downloads (Pure)


We present an investigation of the statistics of velocity gradient related quantities, in particular energy dissipation rate and enstrophy, along the trajectories of fluid tracers and of heavy/light particles advected by a homogeneous and isotropic turbulent flow. The refined similarity hypothesis (RSH) proposed by Kolmogorov and Oboukhov in 1962 is rephrased in the Lagrangian context and then tested along the particle trajectories. The study is performed on state-of-the-art numerical data resulting from numerical simulations up to Reλ∼400 with 20483 collocation points. When particles have small inertia, we show that the Lagrangian formulation of the RSH is well verified for time lags larger than the typical response time τp of the particle. In contrast, in the large inertia limit when the particle response time approaches the integral time scale of the flow, particles behave nearly ballistic, and the Eulerian formulation of RSH holds in the inertial range.
Original languageEnglish
Pages (from-to)066318-1-066318-6
Number of pages6
JournalPhysical review E: Statistical, nonlinear, and soft matter physics
Issue number6
Publication statusPublished - 2009



  • IR-73201
  • METIS-263676

Cite this