  A multi-layer model of an energy length function is developed by employing
recent results of the authors. The theory predicts the complete, mean
streamwise turbulent kinetic-energy profile (MKP), in good agreement with
empirical data for a wide range of Reynolds numbers (Re). In particular, a
critical $Re_\tau$ is predicted, beyond which a scaling anomaly appears and MKP
develops a second peak.

Fluid Dynamics