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The Lie-group-based symmetry analysis, as first proposed in Avsarkisov et al.(2014) and then later modified in Oberlack et al. (2015), to generate invariantsolutions in order to predict the scaling behavior of a channel flow withuniform wall transpiration, is revisited. By focusing first on the resultsobtained in Avsarkisov et al. (2014), we failed to reproduce two key results:(i) For different transpiration rates at a constant Reynolds number, the meanvelocity profiles (in deficit form) do not universally collapse onto a singlecurve as claimed. (ii) The universally proposed logarithmic scaling law in thecenter of the channel does not match the direct numerical simulation (DNS) datafor the presented parameter values. In fact, no universal scaling behavior inthe center of the channel can be detected from their DNS data, as it ismisleadingly claimed in Avsarkisov et al. (2014). Moreover, we will demonstratethat the assumption of a Reynolds-number independent symmetry analysis is notjustified for the flow conditions considered therein. Only when including alsothe viscous terms, an overall consistent symmetry analysis can be provided.This has been attempted in their subsequent study Oberlack et al. (2015). But,also the (viscous) Lie-group-based scaling theory proposed therein isinconsistent, apart from the additional fact that this study of Oberlack et al.(2015) is also technically flawed. The reason for this permanent inconsistencyis that their symmetry analysis constantly involves several unphysicalstatistical symmetries that are incompatible to the underlying deterministicdescription of Navier-Stokes turbulence.

Revisiting the Lie-group symmetry method for turbulent channel flow with wall transpiration