Double exposure, multiple-field particle image velocimetry for turbulent probability density

A particle image velocimeter method is described in which double exposed fields of particles moving in a two-dimensional slice of a steady turbulent flow are photographed repeatedly to build up a statistical ensemble of flow field realizations on a single photographic plate. Each interrogation spot on the plate contains a sample of the probability density function of the two components of velocity that lie in the photographic object plane, assuming paraxial photography. Theory is developed showing how this sample can be measured by two-dimensional spatial correlation analysis, followed by deconvolution to remove the effects of finite particle image size. The probability density measurements are biased inherently against large velocities, but these effects can be minimized and/or corrected.