A new assessment of the second order moment of Lagrangian velocity increments in turbulence

Abstract

The behavior of the second-order Lagrangian structure functions on state-of-the-art numerical data both in two and three dimensions is studied. On the basis of a phenomenological connection between Eulerian space-fluctuations and the Lagrangian time-fluctuations, it is possible to rephrase the Kolmogorov $4/5$-law into a relation predicting the linear (in time) scaling for the second order Lagrangian structure function. When such a function is directly observed on current experimental or numerical data, it does not clearly display a scaling regime. A parameterization of the Lagrangian structure functions based on Batchelor model is introduced and tested on data for $3d$ turbulence, and for $2d$ turbulence in the inverse cascade regime. Such parameterization supports the idea, previously suggested, that both Eulerian and Lagrangian data are consistent with a linear scaling plus finite-Reynolds number effects affecting the small- and large-time scales. When large-time saturation effects are properly accounted for, compensated plots show a detectable plateau already at the available Reynolds number. Furthermore, this parameterization allows us to make quantitative predictions on the Reynolds number value for which Lagrangian structure functions are expected to display a scaling region. Finally, we show that this is also sufficient to predict the anomalous dependency of the normalized root mean squared acceleration as a function of the Reynolds number, without fitting parameters.

References in corpus (4)

• Multifractal statistics of Lagrangian velocity and acceleration in turbulence
• Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation
• Lagrangian Structure Functions in Turbulence: A Quantitative Comparison between Experiment and Direct Numerical Simulation
• Lagrangian statistics in forced two-dimensional turbulence

Cited by in corpus (5)

• Lagrangian Statistics for Navier-Stokes Turbulence under Fourier-mode reduction: Fractal and Homogeneous Decimations
• Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy
• Scaling of acceleration statistics in high Reynolds number turbulence
• Introduction of longitudinal and transverse Lagrangian velocity increments in homogeneous and isotropic turbulence
• How tracer particles sample the complexity of turbulence