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

Monday 8th September 2008 - 16:50 to 17:10
INI Seminar Room 1
Session Chair: 
S Chernyshenko
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons