Processing of three-dimensional particle tracking velocimetry data

Abstract There is a growing necessity to develop advanced data analysis methods capable of dealing with three dimensional data sets, both scalar and vector quantities. In fluid mechanics there are being developed particle tracking methods which allow the determination of the three dimensional spatial distribution of velocity vectors. Most of these methods yield data which is nonuniformly distributed in space causing severe problems with data analyses. In this paper a versatile interpolation method is presented which allows the specification of the data field onto an arbitrary grid. Moreover, the local partial derivatives can be evaluated from the local functional representation which is continuous up to the second derivative throughout the region of interest. The errors associated with the procedure are illustrated relative to the data density and can be expected to be less than 1 % for velocity vector data and less than 5 % for vorticity.