# Power-law profile

From Glossary of Meteorology

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## power-law profile

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 Then where is the mean velocity, For moderate Reynolds numbers,

*l*on height*z*. Here*u*_{*}the friction velocity, ν the kinematic viscosity, and*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.