Correlation Measurements in Turbulence using Digital Fourier Analysis

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Abstract
Time correlations of longitudinal and lateral 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 assumptions of isotropy are approximately satisfied by all of the present measured odd‐order correlation functions, cross correlations, and moments, in contrast with previous measurements by other investigators. The even moments and certain types of even‐order correlations and cross correlations are in excellent quantitative agreement with previous results. The remaining even‐order quantities are considerably different, but generally are closer to the values for an isotropic and Gaussian fluctuating field. Differences in the low‐frequency response of hot‐wire amplifiers and associated instruments may account for the differences between the present data for certain odd‐order correlations and that of earlier investigators.