Logarithmic scaling for fluctuations of a scalar concentration in wall turbulence

TL;DR

This paper demonstrates that the variance of scalar concentration fluctuations in wall turbulence exhibits logarithmic scaling with height, supported by experimental data and a model of attached eddies.

Contribution

It provides experimental evidence and a theoretical model confirming logarithmic scaling of scalar concentration variance in wall turbulence.

Findings

Logarithmic scaling observed for scalar concentration variance.

Experimental validation using heat as a passive scalar.

Model based on attached eddies reproduces the scaling.

Abstract

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.