Analysis of resolution and noise propagation in volumetric PIV measurements of kinetic energy, impulse, and their derivatives

Vortex kinetic energy (KE) and impulse are typical quantities derived from fluid velocity data obtained via volumetric Particle Image Velocimetry (PIV). 3D velocity fields enable direct calculation of these quantities, but PIV measurement also filters the true flow field and inextricably involves noise. In this study, we consider the error in KE and impulse computations in relation to the level of noise, the resolution of the flow feature, smoothing, origin selection, and the field of view. Using a synthetic Hill's vortex, we show that error, for both KE and impulse, is primarily a function of feature resolution. Given a desired percentage of error, we identify the minimum resolution required as a practical reference for experiment design. Further, our results show that typical PIV post-processing is effective in reducing error in KE, while impulse computation is robust, with low unfiltered errors despite high noise levels. Temporal smoothing also has a significant effect on these quantities and their derivatives, which are needed for many formulations of wake power and forces. This study affords us practical recommendations when the computation of such quantities is needed, such as to assess the locomotive performance of swimming and flying organisms.