It has been observed in many previous studies that in the inner region (i.e. y/h < 0.2, where y = any vertical coordinate and h = depth of flow) log-law satisfactorily predicts the velocity but at outer region (i.e. y/h > 0.2) velocity profile deviates from the log-law and a wake parameter is added to velocity profile in order observations follow the log-law. My doubt is that this wake function, does it represent the strength of turbulence in the inviscid region?
The answer to your question, or at least a hint to it, might be found in the first phrase on page 196 of the paper by Donald Coles, "The Law of the Wake in the Turbulent Boundary Layer", a classical in the field that you can download easily from the internet. Other important works that can help you with the answer are the initial paper on turbulence by professor Anatol Roshko.
Good luck,
Marcos A. Ortega
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