On the length-scale of the wind profile

We present the results of an analysis of simultaneous sonic anemometer observations of wind speed and velocity spectra over flat and homogeneous terrain from 10 up to 160 m height performed at the National Test Station for Wind Turbines at Høvsøre, Denmark. The mixing length, l, derived from the wind speed profile, is found to be linearly proportional to the length-scale of turbulence, derived either from the peak of the vertical velocity spectrum, (λm)w, or from a three-dimensional turbulence spectral model, for a range of atmospheric stability conditions, friction Rossby numbers, and within the range of observational heights ((λm)w ∼ 7l).

Under very unstable conditions and above 100 m, the local wind shear is low, and the relation between both length-scales is slightly nonlinear. Mixing-length and wind profile models, which depend on both atmospheric stability and friction Rossby number, generally show better agreement to the observations of the length-scale and wind speed profile than the models from surface-layer theory, which show good agreement with the observations for the first 80 m only.

The results from this analysis demonstrate a close connection between these two types of length-scales. Copyright © 2010 Royal Meteorological Society