Two-Point Descriptions of Wake Turbulence with Application to Noise Prediction

Abstract

Measurements of the four-dimensional two-point correlation tensor of a fully developed airfoil wake are presented. These data allow examination of the characteristic eddies of the turbulence through proper orthogonal decomposition and linear stochastic estimation. A simple generic technique has been developed to extrapolate the correlation tensor function from the Reynolds stress field based on the hypothesis that its form is largely determined by the constraints imposed by inhomogeneity and continuity. Estimates for the plane wake compare favorably with measurements, and, interestingly, proper orthogonal modes and characteristic eddy structures inferred from the estimates are similar to those obtained from measurements. This implies that these measures of the correlation function are largely determined by fairly basic physical information, suggesting some simplification of the turbulence-modeling problem for applications such as aeroacoustics.