Evaluation of scaling laws derived from Lie group symmetry methods in zero-pressure-gradient turbulent boundary layers

Abstract

New scaling laws for turbulent boundary layers recently derived (see Oberlack 2000) using Lie group symmetry methods have been tested against experimental data from the KTH database for zero-pressure-gradient turbulent boundary layers. The most significant new law predicts an exponential variation of the mean velocity defect in the outer (wake) region. It was shown to fit the experimental data very well over a large part of the boundary layer, from the outer part of the overlap region to about half the boundary layer thickness ($\delta_{99}$). In the outermost part of the boundary layer the velocity defect falls more rapidly than predicted by the exponential law. This can partly be attributed to intermittency in that region but the main cause stems from non-parallel effects that are not accounted for in the derivation of the exponential law. The two-point correlation function behaviour in the outer region, where an exponential velocity defect law is observed, was found to be very different from that derived under the assumption of parallel flow. It is found to be plausible that this indeed can be attributed to non-parallel effects. A small modification of the innermost part of the log-layer in the form of an additive constant within the log-function is predicted by the Lie group symmetry method. A qualitative agreement with such a behaviour just below the overlap region was found. The derived scaling law behaviour in the overlap region for the two-point correlation functions was also verified by the experimental data.