Works by Barenblatt and others have shown that besides the logarithmic law of the wall — the limit for infinite Reynolds numbers — there exist power-law solutions, which are dependent on the Reynolds number. 
In 1996, Cipra submitted experimental evidence in support of these power-law descriptions. This evidence itself has not been fully accepted by other experts. In 2001, Oberlack claimed to have derived both the logarithmic law of the wall, as well as power laws, directly from the Reynolds-averaged Navier–Stokes equations, exploiting the symmetries in a Lie group approach. However, in 2014, Frewer et al. refuted these results.