Scaling of acceleration statistics in high Reynolds number turbulence

TL;DR

This paper investigates how acceleration statistics scale in high Reynolds number turbulence, combining literature data with new simulations, revealing discrepancies with existing models and proposing a relation to Eulerian statistics.

Contribution

It demonstrates that acceleration variance scaling deviates from multifractal predictions at high Reynolds numbers and introduces a new relation linking acceleration to Eulerian velocity gradients.

Findings

Acceleration variance departs from multifractal model predictions at high Reynolds numbers.

A new relation between acceleration variance and Eulerian velocity gradients is validated.

Lagrangian intermittency may need independent modeling from Eulerian intermittency.

Abstract

The scaling of acceleration statistics in turbulence is examined by combining data from the literature with new data from well-resolved direct numerical simulations of isotropic turbulence, significantly extending the Reynolds number range. The acceleration variance at higher Reynolds numbers departs from previous predictions based on multifractal models, which characterize Lagrangian intermittency as a naive extension of Eulerian intermittency. The disagreement is even more prominent for higher-order moments of the acceleration. Instead, starting from a known exact relation, we relate the scaling of acceleration variance to that of Eulerian fourth-order velocity gradient and velocity increment statistics. This prediction is in excellent agreement with the variance data. Our work highlights the need for models that consider Lagrangian intermittency independent of the Eulerian counterpart.