logarithmic velocity profile
Near aerodynamically smooth surfaces, the result is
that is, the logarithmic velocity profile, where u*
is the friction velocity
and ν the kinematic viscosity
≅ 0.4 and has been called the Kármán constant or von Kármán's constant
. The equation fails for a height z
sufficiently close to the surface. For aerodynamically rough flow, molecular viscosity
becomes negligible. The profile is then z0
is a constant related to the average height ε of the surface irregularities by z0
= ε/30 and is called the aerodynamic roughness length
. Another derivation of the logarithmic profile was obtained by Rossby under the assumption that for fully rough flow the roughness affects the mixing length
only in the region where z
are comparable. Then l
For statically nonneutral conditions, a stability
correction factor can be included (see
equation in definition of aerodynamic roughness length
Haugen, D. A. 1973. Workshop on Micrometeorology. Amer. Meteor. Soc., 392 pp.
Sutton, O. G. 1953. Micrometeorology. sect. 3.9.
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