From AMS Glossary
A reference wind velocity defined by the relation
where τ is the Reynolds stress, ρ the density, and u* friction velocity.
Using the surface kinematic momentum fluxes in the x and y directions (
) to represent surface stress, the friction velocity can be written as
It is usually applied to motion near the ground where the shearing stress is often assumed to be independent of height and approximately proportional to the square of the mean velocity. The friction velocity is, therefore, exactly the velocity for which this square law would be valid.
Sutton, O. G. 1953. Micrometeorology. p. 76.