### A simple model for the log-law region of a boundary layer

**Davidson, P ***(Cambridge )*

Monday 08 September 2008, 16:50-17:10

Seminar Room 1, Newton Institute

#### Abstract

We build on the work of Davidson, Krogstad & Nickels (JFM, 2006) and propose an elementary model for the log-law region of a boundary-layer. The model is remarkably simple, contains only one free parameter, 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. Little else is assumed. Despite its naivety, the model is an excellent fit to experimental data for the k-1 law of the one-dimensional, longitudinal spectrum, F11(k), and also to F11(k), in the inertial range. It is also an excellent fit to experimental data for the real-space analogue of the k-1 law; that is, the logarithmic law for the longitudinal structure-function.

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