Local Isotropy in the Turbulent Wake of a Cylinder

Abstract

To investigate the validity of Kolmogoroff's theory of local isotropy, a series of turbulence measurements have been made in the wake of a circular cylinder, and the results have been compared with the predictions of the theory. Using a cylinder of 0.953 cm. diameter in an air-stream of velocity 1,280 cm. sec.^-1, measurements have been made of the mean squares of the spatial derivatives in the mean-stream direction of the three components of the turbulent velocity fluctuation, and also of the skewness and flattening factors of the statistical distributions of these derivatives. Observations were taken at three traverses across the wake, respectively at 80, 120, and 160 cylinder diameters down-stream from the cylinder. Except in the immediate neighbourhood of the wake centre, the turbulent flow is observed to be intermittent, consisting of regions of fully developed turbulent flow separated by comparatively sharp boundaries from regions of almost completely laminar motion. If an "intermittency factor " is introduced to describe this phenomenon, and if inside each turbulent region local isotropy exists, then all the experimental results are consistent with the theory of local isotropy, and in agreement with previous measurements in flows possessing ordinary isotropy. It is concluded that, within the boundaries of the turbulent regions, local isotropy in the sense used by Kolmogoroff exists, and that the theory is applicable to this example of shear flow. The general applicability of the theory to turbulent shear flow at high Reynolds numbers must be considered very probable.