Functional binning: improving convergence of Eulerian statistics from Lagrangian particle tracking

In the analysis of Lagrangian particle tracking data, ensemble averaging with spatial bins is used to generate Eulerian flow statistics. Due to the scattered nature of the particles over independent snapshots, the possible spatial resolution is directly dependent on the measured particle position accuracy and the amount of available data. This requires a balance between convergence of the underlying statistic and the bin resolution. Current binning approaches use the velocity information of the particle positions at single time steps directly and do not exploit the additional information available from the temporal filtering of the tracking process. We present a novel functional approach to the binning procedure that extracts all available information from the particle tracks and improves convergence speed. For a given experiment this allows for higher resolution of flow statistics than classical approaches or alternatively to reduce the necessary amount of data required for a given resolution. Furthermore, uncertainty measures from the particles position, velocity and acceleration can be propagated directly by weighting coefficients.