The friction velocity (also known as the shear-stress velocity), u*, of a flow is defined by the relation:
where τ is the shear stress and r the fluid density. This quantity has the dimensions of velocity and is frequently encountered in the study of Boundary Layers. For turbulent flow it is approximately constant in the region near to a wall, and in the atmosphere, this region extends over the lowest several metres. The flow velocity in the boundary layer is commonly expressed in terms of the friction velocity and the height, z, as:
where z0 is the roughness length. κ is an empirical constant known as the von Kármán constant and is found to have a value of κ ≈ 0.35 for all cases of turbulent flow. The derivation of this formula is given in, for example, Holton (1979) and Streeter and Wylie (1983).
Holton, J. R. (1979) An Introduction to Dynamic Meterorology, Academic Press, New York.
Streeter, V. L. and Wylie, E. B. (1983) Fluid Mechanics, McGraw-Hill, Singapore.