Lagrangian Curvature Statistics from Gaussian Subensembles in Turbulent Flows

Abstract

A salient feature of fully turbulent flows far from onset is the intermittent occurrence of extreme fluctuations at small spatial and temporal scales. These have a qualitative and quantitative effect on the instantaneous curvature of a tracer particle trajectory as an intrinsically multi-scale observable. Here, we provide a complete statistical description of the curvature of tracer particle trajectories in turbulent flows that includes and quantifies intermittency effects. We derive an exact expression and a closed-form approximation for the curvature probability density function, both agree well with data obtained from laboratory experiments of different types of turbulent flows, and quantify the generic behavior of the system. The method can be extended to more complex systems such as plasma turbulence.