Using persistent accelerations to determine one-particle statistics in turbulence

Lagrangian particles frequently encounter extreme acceleration events in fully developed turbulence. Intense small-scale structures such as vorticity filaments can give rise to acceleration events exceeding the typical root-mean-squared fluctuations by orders of magnitude. Here, we introduce the notion of persistent Lagrangian acceleration, quantified by the squared Lagrangian acceleration coarse-grained over a viscous time scale. Conditioning Lagrangian particle data from direct numerical simulations on this coarse-grained acceleration, we find remarkably simple, close-to-Gaussian statistics for a range of Reynolds numbers. Based on this observation, which provides a new perspective on the Lagrangian refined similarity hypothesis, we develop a theory of Lagrangian single-particle statistics covering the acceleration, velocity increments as well as single-particle dispersion.