Scaling of Lagrangian acceleration in isotropic turbulence at high Reynolds numbers

The acceleration of a fluid element in a turbulent flow, given by the Lagrangian derivative of the velocity, and resulting from balance of forces acting on it, is the simplest description of its motion. Hence, the statistics of acceleration are of paramount importance from both a fundamental viewpoint and for modeling purposes. Here, we examine the scaling of acceleration moments 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 an 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 urgent need for models that consider Lagrangian intermittency independent of the Eulerian counterpart.