Within wall turbulence, there is a sublayer where the mean velocity and the variance of velocity fluctuations vary logarithmically with the height from the wall. This logarithmic scaling is also known for the mean concentration of a passive scalar. By using heat as such a scalar in a laboratory experiment of a turbulent boundary layer, the existence of the logarithmic scaling is shown here for the variance of fluctuations of the scalar concentration. It is reproduced by a model of energy-containing eddies that are attached to the wall.

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We validated a model that was recently derived by Mouri (2017) for the twopoint correlation function of the streamwise velocity fluctuation u in wallturbulence by using experimental boundary layer data. The model expresses the correlation function as the superposition of the contributions from the main eddies located at the height where the correlation is evaluated and the attached eddies located above. These contributions were quantified as a function of r/y, where r is the streamwise distance and y is the height from the wall, and evaluated by using the data. The contribution from the main eddies exhibits logarithmic dependence for r/y=O(1), and that from the attached eddies occurs only for r/y=O (10), where it also decays logarithmically with r/y. Furthermore, the model was extended to include the wall-normal energy flux due to turbulent convection, by assuming that the flux consists of the selfsimilar transfer of main eddies, and the transfer of the larger attached eddies. It was found that the flux of u 2 was expressed well by the extended model, and the two contributions were evaluated using the experimental data. Both types of eddies are strongly convected upward and downward; however, for the attached eddies, most of the fluxes in the opposite directions cancel out, leading to a reduced contribution to the net flux.

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