Abstract
In this paper, we discuss several recent theoretical approaches to wall-bounded flows such as turbulent boundary layers and pipe flows. Specifically, the power law theories by Barenblatt and George and a higher-order approach proposed by Buschmann and Gad-el-Hak are discussed. By employing probably the best data sets currently available worldwide, we uncover the qualities of these approaches. The outcome shows that the mean-velocity profile of turbulent wall-bounded flows is much more complex than the classical logarithmic law or a simple power law. A Reynolds number dependence of the mean profile persisting for arbitrarily high but finite Reynolds numbers seems to be highly likely. Both experimental and theoretical efforts are needed to solve the currently open questions.
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