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The study by Oberlack et al. (2006) consists of two main parts: a directnumerical simulation (DNS) of a turbulent plane channel flow with streamwiserotation and a preceding Lie-group symmetry analysis on the two-pointcorrelation equation (TPC) to analytically predict the scaling of the meanvelocity profiles for different rotation rates. We will only comment on thelatter part, since the DNS result obtained in the former part has already beencommented on by Recktenwald et al. (2009), stating that the observed mismatchbetween DNS and their performed experiment is possibly due to the prescriptionof periodic boundary conditions on a too small computational domain in thespanwise direction. By revisiting the group analysis part in Oberlack et al.(2006), we will generate more natural scaling laws describing better the meanvelocity profiles than the ones proposed. However, due to the statisticalclosure problem of turbulence, this improvement is illusive. As we willdemonstrate, any arbitrary invariant scaling law for the mean velocity profilescan be generated consistent to any higher order in the velocity correlations.This problem of arbitrariness in invariant scaling persists even if we wouldformally consider the infinite statistical hierarchy of all multi-pointcorrelation equations. The closure problem of turbulence simply cannot becircumvented by just employing the method of Lie-group symmetry analysis alone:as the statistical equations are unclosed, so are their symmetries! Hence, an apriori prediction as how turbulence scales is thus not possible. Only aposteriori by anticipating what to expect from numerical or experimental datathe adequate invariant scaling law can be generated through an iterativetrial-and-error process. Finally, apart from this issue, also severalinconsistencies and incorrect statements to be found in Oberlack et al. (2006)will be pointed out.

On the use of applying Lie-group symmetry analysis to turbulent channel flow with streamwise rotation