Some considerations on the accuracy and frequency response of some derivative filters applied to particle image velocimetry vector fields

This paper concerns the computation of derivatives from particle image velocimetry (PIV) velocity fields with the goal of obtaining the vorticity component normal to the plane. A variety of derivative schemes are characterized by their transfer function, taking into account the truncation and noise amplification. The PIV measurement noise is supposed to be a white one in the Fourier space. A spectral approach is used in order to choose the best filter for turbulent flows. The derivative spectra are discussed. An application is presented on a real turbulent flow with two interrogation window sizes and different derivative schemes. The most significant schemes are also applied to a velocity field containing a single vortex. A comparison of the maximum of vorticity obtained with each scheme and through a least-square tit with an Oseen vortex, allows us to quantify the effect of the band pass filter and to select the best scheme.