Lagrangian curvature statistics from Gaussian sub-ensembles in turbulent von-Kármán flow

A salient feature of fully turbulent flows far from onset is the intermittent occurrence of extreme fluctuations at small spatial and temporal scales. Here, we derive an expression for the curvature probability density function (pdf) for the ensemble of tracer particle trajectories in isotropic turbulence that includes effects of spatio-temporal intermittency. We obtain a master curve for the pdf for near-Gaussian sub-ensembles, generated by conditioning on the squared acceleration coarse-grained over a few viscous time units (Bentkamp, Lalescu, Wilczek, Nat. Comm., 10, 3550 (2019)), where an analytic form of the pdf is known (Xu, Ouellette, Bodenschatz, Phys. Rev. Lett., 98, 050201 (2007)). Using this expression, we calculate the pdf for the full ensemble resulting in a re-scaled version the master curve. The scaling factor is related to moments of the coarse-grained acceleration, and thus includes the effect of spatio-temporal intermittency. The derived pdf agrees qualitatively and quantitatively with the curvature pdf sampled from tracer particle data in von-Kármán flow obtained by Shake-The-Box processing (Schanz, Gesemann, Schröder, Exp. Fluids 57:70 (2016)).