On Lagrangian single-particle statistics

Abstract

The length distribution of streamline segments in homogeneous isotropic decaying turbulence Phys. Fluids 24, 045104 (2012) Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence Phys. Fluids 24, 035108 (2012) Near-field investigation of turbulence produced by multi-scale grids Phys. Fluids 24, 035103 (2012) Reynolds number effect on the velocity increment skewness in isotropic turbulence Phys. Fluids 24, 015108 (2012) Spectral approach to finite Reynolds number effects on Kolmogorov's 4/5 law in isotropic turbulence Phys. Fluids 24, 015107 (2012) In turbulence, ideas of energy cascade and energy flux, substantiated by the exact Kolmogorov relation, lead to the determination of scaling laws for the velocity spatial correlation function. Here we ask whether similar ideas can be applied to temporal correlations. We critically review the relevant theoretical and experimental results concerning the velocity statistics of a single fluid particle in the inertial range of statistically homogeneous, stationary and isotropic turbulence. We stress that the widely used relations for the second structure function, D 2 (t) ≡ [v(t) − v(0)] 2 ∝ εt, relies on dimensional arguments only: no relation of D 2 (t) to the energy cascade is known, neither in two-nor in three-dimensional turbulence. State of the art experimental and numerical results demonstrate that at high Reynolds numbers, the derivative d D 2 (t) dt has a finite non-zero slope starting from t ≈ 2τ η . The analysis of the acceleration spectrum A (ω) indicates a possible small correction with respect to the dimensional expectation A (ω) ∼ ω 0 but present data are unable to discriminate between anomalous scaling and finite Reynolds effects in the second order moment of velocity Lagrangian statistics. C 2012 American Institute of Physics.

Flight–crash events in turbulence

“…Different γ contribute different velocity moments. Landau-Obukhov phenomenology (14) suggests δV ðτÞ ' ð«τÞ 1=2 , which physically corresponds to velocity diffusion under the action of random short-correlated forces. If particle acceleration (energy increase) would proceed in this way, one would expect hp 2 i ∝ ha 2 i ∝ R λ .…”

“…The kinetic energy per unit mass of the fluid is simply EðtÞ = ð1=2ÞV 2 ðtÞ, where VðtÞ is the velocity of a given fluid element. It should be stressed that detecting irreversibility from the motion of a single particle requires going beyond velocity structure functions, defined as the moments of velocity differences along trajectories, VðtÞ − Vð0Þ, whose statistical properties are invariant under the t → − t transformation (14).…”

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

“…This is another route to explain the anomalous scaling of the acceleration variance as a function of Re λ , which has been investigated in [15] and which is not in contradiction with any exact scaling law in Lagrangian turbulence. In [15], the intermittent correction γ was obtained from a fit of the scaling of (10). [ 11,30,31,[40][41][42].…”

“…not Reynolds number dependentdeparture of S 2 (τ ) from the linear scaling predicted by (2). For instance, in [15] it was investigated the possibility that anomalous scaling develops already for S 2 (τ ) and it was showed that also this option is not inconsistent with the data.…”

“…Alternatively, in [15], a small modification of the linear scaling for the second order structure function has been proposed on the basis of the observed behavior of the acceleration spectrum. While further data are needed to definitely discriminate between anomalous scaling or finite Reynolds number effects in the second order moment, we point out that the simple parameterization here proposed gives very good results without invoking any intermittent correction.…”