Velocity gradients statistics along particle trajectories in turbulent flows: the refined similarity hypothesis in the Lagrangian frame

Abstract

We present an investigation of the statistics of velocity gradient related quantities, in particluar 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 Re~400 with 2048^3 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 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.

7 pages, 7 figures; Physical Review E (accepted Dec 7, 2009)

References in corpus (8)

• Universal intermittent properties of particle trajectories in highly turbulent flows
• Lagrangian dynamics and statistical geometric structure of turbulence
• Dimensionality and morphology of particle and bubble clusters in turbulent flow
• Multifractal concentrations of inertial particles in smooth random flows
• Lagrangian Structure Functions in Turbulence: A Quantitative Comparison between Experiment and Direct Numerical Simulation
• Quantifying turbulence induced segregation of inertial particles
• PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow,
• Multi-scale model of gradient evolution in turbulent flows

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