Ensemble decomposition for Lagrangian turbulence: Reynolds number trends and modeling

Previous work (Bentkamp et al. Nat. Commun. 10:3550, 2019) has shown that Lagrangian statistics in homogeneous isotropic turbulence can be approximately decomposed into Gaussian sub-ensembles by considering statistics conditioned on the squared acceleration coarse-grained over a viscous time scale. In this framework, each sub-ensemble is determined by the conditional Lagrangian velocity autocorrelation function. Using high-fidelity direct numerical simulation (DNS) data, we here explore Reynolds-number trends of the conditional correlation functions. Our evaluation shows that, for short times, the conditional correlation functions can be approximately collapsed for different Reynolds numbers by appropriate rescaling, enabling modeling approaches across Reynolds numbers. We present results on such a model along with comparisons to DNS data.