Multi-Point Lagrangian Velocity Estimates

Abstract

Micron-sized particles of solid deuterium are suspended in superfluid 4 He (He II) and their time-dependent positions are captured by using the particle tracking velocimetry technique. As the computation of the particle velocities from the obtained positions can be noisy, mainly due to experimental uncertainties, we compare here four different numerical approaches to estimate the velocities. We choose, as a test case, the flow of He II occurring between two grids oscillating in phase, which, in the range of investigated parameters, display classicallike features, very similar to those found in turbulent flows of viscous fluids. We focus on algorithms that consider multiple particle positions for the estimation of a single velocity. Although the velocities computed by the chosen procedures are relatively similar, we find that the statistical distributions of the corresponding velocity increments, i.e., coarse-grained accelerations, depend on the choice of the algorithm and its parameters in a more pronounced way than in the case of velocities. It follows therefore that the numerical approach employed to estimate Lagrangian velocity increments should be chosen carefully on the basis of the physical problem being investigated.