Angular multiscale statistics of Lagrangian trajectories in turbulence

TL;DR

This paper investigates the multiscale statistical properties of Lagrangian trajectories in turbulence by analyzing the angle between particle displacements, revealing power-law behaviors and self-similar distributions indicative of complex turbulence dynamics.

Contribution

It introduces a novel analysis of the angular statistics of particle trajectories, demonstrating power-law scaling and providing an analytical model for the distribution.

Findings

Two power-law regimes in the angle evolution with time lag

Self-similar probability density function of directional changes

Analytical model assuming Gaussianity and independence fits data well

Abstract

The angle between subsequent particle displacement increments is evaluated as a function of the timelag in isotropic turbulence. It is shown that the evolution of this angle contains two well-defined power-laws, reflecting the multi-scale dynamics of high-Reynolds number turbulence. The proba-bility density function of the directional change is shown to be self-similar and well approximated by an analytically derived model assuming Gaussianity and independence of the velocity and the Lagrangian acceleration.