The potential flow bounded by a mixing layer and a solid surface

Abstract
Phillips's ( Proc. Camb. Phil. Soc . 51, 220 (1955)) analysis of the potential 'near field' forced by a turbulent shear layer is extended to include calculation of velocity spectra, spatial correlations and the effect of a solid surface at a finite distance from the shear layer. In the region away from the influence of the wall the theory predicts that correlation scales depend principally on the effective distance from the turbulence. This result suggests that the large correlation scales measured outside turbulent mixing layers do not necessarily demonstrate the essential tow-dimensionality of the large turbulent eddies and shows why mixing layers are more influenced by potential flow effects than are other shear layers. The detailed comparison of the theory to measurements made outside a high Reynolds number single-stream turbulent mixing layer results in an unphysical negative regions are caused by an error in a basic assumption of the theory. However, all the measured correlation scales appear to increase linearly with distance from the turbulence and therefore are consistent with the main result of the analysis. As the potential flow becomes affected by the wind tunnel floor, u 2 — and w 2 — are amplified significantly more than the theory predicts, while v 2 — is not attenuated. These discrepancies are attributed partly to the streamwise inhomogeneity of the flow, which was not incorporated into the analysis.