# Persistent accelerations disentangle Lagrangian turbulence

## TL;DR

This paper introduces persistent Lagrangian acceleration to simplify the complex, scale-dependent statistics of particles in turbulence, revealing near-Gaussian behavior and enabling a new theoretical framework for single-particle turbulence statistics.

## Contribution

It presents a novel approach using coarse-grained acceleration to decompose complex turbulence statistics into simpler, near-Gaussian sub-ensembles, advancing understanding of Lagrangian turbulence.

## Key findings

- Close-to-Gaussian statistics for particle acceleration across Reynolds numbers
- Decomposition of complex turbulence statistics into simpler sub-ensembles
- Development of a theoretical framework for single-particle turbulence statistics

## Abstract

Particles in turbulence frequently encounter extreme accelerations between extended periods of quiescence. The occurrence of extreme events is closely related to the intermittent spatial distribution of intense flow structures such as vorticity filaments. This mixed history of flow conditions leads to very complex particle statistics with a pronounced scale dependence, which presents one of the major challenges on the way to a non-equilibrium statistical mechanics of turbulence. Here, we introduce the notion of persistent Lagrangian acceleration, quantified by the squared particle acceleration coarse-grained over a viscous time scale. Conditioning Lagrangian particle data from simulations on this coarse-grained acceleration, we find remarkably simple, close-to-Gaussian statistics for a range of Reynolds numbers. This opens the possibility to decompose the complex particle statistics into much simpler sub-ensembles. Based on this observation, we develop a comprehensive theoretical framework for Lagrangian single-particle statistics that captures the acceleration, velocity increments as well as single-particle dispersion.