Autocorrelation function for estimating static pressure fluctuation intensity in incompressible homogeneous turbulence under an intermediate Reynolds number

This study presents a simple form of an autocorrelation function that estimates the relative static pressure fluctuation intensity in the intermediate range of Reynolds numbers. When the Reynolds number is high or low, values of relative static pressure fluctuation intensity are each derived as simple values. This study attempts to estimate the intensity between high and low Reynolds numbers. Using the joint-normal approximation in the velocity field allows the relative static pressure fluctuation intensity to be given by integrating a function based on the autocorrelation function. For high and low Reynolds numbers, the autocorrelation function is given as exponential and Gaussian profiles, respectively. This study adds a higher-order term to these functions using Gram-Charlier and power series expansion. In the incompressible turbulence, a correlation function has to satisfy the continuity equation. Also, there is a defined relationship between the integral scale and the Taylor microscale derived from the autocorrelation function. This study investigates an autocorrelation function that satisfies these conditions. The value of one constant included in the present autocorrelation function shown in this study is derived as the appropriate value based on these conditions.