A cross-correlation technique for velocity field extraction from particulate visualization

Abstract

A rapid time series of photographs of the horizontal cross-sections of several y ⁺ locations were taken of a turbulent open-channel water flow with Re _d = 3,900. A pair of photographic images were obtained with a time difference of 1.3 v/u ²_τ at each y ⁺ locations. The pictures were digitized into 8 bit data with a spatial resolution of 2.5 viscous scales. Instead of identifying discrete particles, a variable interval spatial correlation technique was used to extract the velocity components. With this technique, two-dimensional spatial cross-correlations of the illumination intensities were taken between a pair of picture images. The correlations were taken over small areas and the peak of the correlation coefficients were used to obtain the convection velocity yielding the u and w components of velocity. Some statistical properties were calculated and are shown to be comparable with previous data. Spatial correlations of the velocity components revealed some unique characteristics related to the structure of turbulence.