Shear velocity

The friction velocity is a measure of the hydrodynamic shear stress exerted by a layer of a fluid flowing in an adjacent layer or a boundary surface. It is calculated from the shear stress on

With the density of the fluid.

Media in turbulent shear stress is dominated by the turbulent transport. The components of the shear stress vector are then calculated from the elements of the Reynolds Schubspannungstensors:

Wherein and the two velocity components parallel (x and y directions ) and vertically ( z-direction) to the boundary surface is. The primed quantities as there are deviations from the mean. The two covariances and can thereby also be interpreted as the turbulent flow in the z direction of the momentum in the x and y direction. The friction velocity is the root of the sum of this vector:

In the derivation of the log wind profile across the Mischungsweglängenansatz by Prandtl is assumed that the mean wind direction and the direction of the shear stress coincide. The coordinate system is defined such that the x axis is parallel to the mean wind direction, and thus, and it is made the assumption that is. In this case: