Statistics of 3-dimensional Lagrangian turbulence

TL;DR

This paper presents a superstatistical model for 3D Lagrangian turbulence that accurately predicts experimental velocity and acceleration statistics, scaling exponents, and temporal correlations in high-Reynolds number flows.

Contribution

The paper introduces a novel superstatistical dynamical model that aligns closely with experimental data on Lagrangian turbulence, including scaling laws and statistical dependencies.

Findings

Model predictions match experimental velocity and acceleration PDFs.

The model accurately reproduces Lagrangian scaling exponents.

It explains the lag between enstrophy and dissipation observed in turbulence.

Abstract

We consider a superstatistical dynamical model for the 3-d movement of a Lagrangian tracer particle embedded in a high-Reynolds number turbulent flow. The analytical model predictions are in excellent agreement with recent experimental data for flow between counter-rotating disks. In particular, we calculate the Lagrangian scaling exponents zeta_j for our system, and show that they agree well with the measured exponents reported in [X. Hu et al., PRL 96, 114503 (2006)]. Moreover, the model correctly predicts the shape of velocity difference and acceleration probability densities, the fast decay of component correlation functions and the slow decay of the modulus, as well as the statistical dependence between acceleration components. Finally, the model explains the numerically [P.K. Yeung and S.B. Pope, J. Fluid Mech. 207, 531 (1989)] and experimentally observed fact [B.W. Zeff et al., Nature 421, 146 (2003)] that enstrophy lags behind dissipation.