Abstract
© 2009 TSFP4 Symposium. All Rights Reserved. We build on the work of Davidson et al. (2006) and propose an elementary model for the log-law region of a boundary-layer. The model contains only one free parameter (which we set equal to unity) and assumes very little about the shape of the boundary-layer eddies. The physical content of the model is simple: we assume that the two-point statistics of the streamwise velocity fluctuations know about the presence of the wall only to the extent that, over a range of eddy sizes, it imposes a kinetic energy scale proportional to the square of the shear velocity. Classic Kolmogorov phenomenology is assumed for the small scales. The model is an excellent fit to experimental data for the k−1 law of the one-dimensional, longitudinal spectrum, Φuu (k), and also to Φuu (k) in the inertial range. In addition, the model predicts the cross-stream variation of the variance of the streamwise velocity fluctuations, u2x. Our prediction of the cross-stream variation of u2x differs from all other theories in that it incorporates a ln (P/) correction, where P and are the production and dissipation of energy respectively.
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