Correlation measurements in grid turbulence using digital harmonic analysis

Abstract

Two-point time correlations up to eighth order of longitudinal velocity fluctuations in grid-generated turbulence have been measured using linearized hot-wire anemometry, digital sampling, and a high-speed digital computer. A novel feature of the present measurements is the adoption of digital Fourier analysis, using the recently developed fast-Fourier transform method. The joint probability density function for the velocity fluctuations at two points separated in time is found to be significantly non-Gaussian. All measured even-order correlations are nearly identical with those reported by Frenkiel & Klebanoff (1967 a, b), and higher-order correlations may be accurately predicted from the second-order correlation by assuming a Gaussian joint probability density. All individual odd-order correlations are substantially different from those reported by Frenkiel & Klebanoff. In particular, all mean values of odd powers of the fluctuating velocity are nearly zero, and the correlations are nearly antisymmetrical functions of the time delay as would be the case for purely isotropic homogeneous turbulence. In spite of the large difference between the individual measured odd-order correlations and previous measurements, quantities such as the skewness and skewness factor derived from certain combinations of the correlations are found to be quite insensitive to observed differences in the form of the correlations and are very similar to previous measurements.