Role of data uncertainties in identifying the logarithmic region of turbulent boundary layers

Abstract

Composite expansions based on the log-law and the power-law were used to generate synthetic velocity profiles of zero pressure gradient turbulent boundary layers (TBLs) in the range of Reynolds number \(800 \le Re_{\theta } \le 860{,}000,\) based on displacement thickness and freestream velocity. Several artificial errors were added to the velocity profiles to simulate typical measurement uncertainties. The effects of the simulated errors were studied by extracting log-law and power-law parameters from all these pseudo-experimental profiles. Various techniques were used to establish a measure of the deviations in the overlap region. When parameters extracted for the log-law and the power-law are associated with similar levels of deviations with respect to their expected values, we consider that the profile leads to ambiguous conclusions. This ambiguity was observed up to \(Re_{\theta }=16{,}000\) for a 4 % dispersion in the velocity measurements, up to \(Re_{\theta }=8.6 \times 10^{5}\) for a 400 \(\upmu\)m uncertainty in probe position (in air flow at atmospheric pressure), and up to \(Re_{\theta }=32{,}000\) for 3 % uncertainty in the determination of \(u_{\tau }.\) In addition, a new method for the determination of the log-law limits is proposed. The results clearly serve as a further note for caution when identifying either a log or a power-law in TBLs. Together with a number of available studies in the literature, the present results can be seen as a additional reconfirmation of the log-law.