# How tracer particles sample the complexity of turbulence

## TL;DR

This paper develops a theoretical framework to understand how tracer particles sample turbulence, validated through numerical simulations, enabling better modeling of transport phenomena in complex turbulent flows.

## Contribution

It introduces a probabilistic model linking particle velocity fluctuations to spatial field fluctuations, advancing the understanding of particle sampling in turbulence.

## Key findings

- The model accurately predicts particle velocity statistics from flow field data.
- Numerical simulations confirm the theoretical predictions across different Reynolds numbers.
- The approach facilitates improved transport modeling in turbulent flows.

## Abstract

On their roller coaster ride through turbulence, tracer particles sample the fluctuations of the underlying fields in space and time. Quantitatively relating particle and field statistics remains a fundamental challenge in a large variety of turbulent flows. We quantify how tracer particles sample turbulence by expressing their temporal velocity fluctuations in terms of an effective probabilistic sampling of spatial velocity field fluctuations. To corroborate our theory, we investigate an extensive suite of direct numerical simulations of hydrodynamic turbulence covering a Taylor-scale Reynolds number range from 150 to 430. Our approach allows the assessment of particle statistics from the knowledge of flow field statistics only, therefore opening avenues to a new generation of models for transport in complex flows.