Limiting behavior of the transverse turbulent velocity fluctuations close to a wall

In previous studies of turbulent flow in a pipe the component of the fluctuating velocity gradient at the wall in the direction of mean flow has been measured by determining the limiting current to a small rectangular polarized electrode mounted flush with the wall and oriented perpendicular to the flow. By measuring the limiting current at an electrode at 12 to 20° as well as at 90° the root-mean-squared value of the component in the transverse direction has been estimated to be about 0.087 of the time-averaged velocity gradient at the wall. This is in agreement with recent photographic measurements of solid particles close to a wall made by Fowles. These results suggest that the limiting behavior of the eddy diffusion coefficient close to a wall is such that ∊ → y3 as y → 0, unless fluctuations in the mass transfer rate are uncorrelated with fluctuations in the gradient of the transverse velocity component.