Estimating two-point statistics from derivatives of a signal containing noise: Application to auto-correlation functions of turbulent Lagrangian tracks.

This article describes a method for calculating moments and correlation functions of signal derivatives, which were rid of experimental noise without the use of filtering operations. The method is based on the computation of the ensemble-average of different time (or spatial) increments of the signal. The hypotheses are that the noise is white and not correlated with the signal; however, the method is also shown to work with colored noise. The method is first developed, considering white noise, and benchmarked with synthetic trajectories containing noise with variable signal-to-noise ratios. It is then tested on experimental trajectories in the context of Lagrangian tracking of particles in turbulent flows, either containing a short-correlated noise or a colored noise.

Equilibrium position of a rigid sphere in a turbulent jet: A problem of elastic reconfiguration.

The position of floating spheres trapped within an immersed turbulent water jet is investigated. Using the self-similarity properties of the jet velocity profile, the equilibrium problem is formulated in a rescaled space where the sphere is static and deformable. This approach is found to be related to a problem of elastic reconfiguration where elasticity arises here from the geometry of the flow instead of an actual deformation of a body.