power-law profile

A formula for the variation of wind with height in the surface boundary layer. It is an alternative to the logarithmic velocity profile, and the assumptions are the same, with the exception of the form of the dependence of mixing length l on height z. Here

Then

where is the mean velocity, u_* the friction velocity, ν the kinematic viscosity, and

For moderate Reynolds numbers, p = 6/7 (the seventh-root profile) is empirically verified, but for large Reynolds numbers p is between this value and unity. It is to be noted that if is proportional to z^m, and if the stress is assumed independent of height, then the eddy viscosity ν_e is proportional to z^1-m. These relations are known as Schmidt’s conjugate-power laws.
Sutton, O. G. 1953. Micrometeorology. 78–85.