The viscous sublayer revisited-exploiting self-similarity to determine the wall position and friction velocity

In experiments using hot wires near the wall, it is well known that wall interference effects between the hot wire and the wall give rise to errors, and mean velocity data from the viscous sublayer can usually not be used to determine the wall position, nor the friction velocity from the linear velocity distribution. Here, we introduce a new method that takes advantage of the similarity of the probability density distributions (PDF) or rather the cumulative distribution functions (CDF) in the near-wall region. By using the velocity data in the CDF in a novel way, it is possible to circumvent the problem associated with heat transfer to the wall and to accurately determine both the wall position and the friction velocity. Prior to its exploitation, the self-similarity of the distribution functions of the streamwise velocity fluctuations within the viscous sublayer is established, and it is shown that they can accurately be described by a lognormal distribution.