Long Time Memory of Lagrangian Acceleration Statistics in 2D and 3D Turbulence

In this paper we report on a comparison of Lagrangian acceleration statistics in the direct energy cascade of three-dimensional turbulence and the corresponding observables for the case of the inverse energy cascade in two dimensions. We focus on the time scales describing the memory of the acceleration statistics of a tracer particle. We show that for both systems the Markov time scale, which is an indicator for the length of the memory of a stochastic process, is in the order of magnitude of the Lagrangian integral time scale. We also show that the decorrelation time for the cross-correlation between the squared components of the acceleration is larger than the integral time scale.