Question

The logarithmic wind profile assumes horizontal homogeneity and temporal stationarity. Give two examples how those assumptions might be violated here.

Answer 1

Stable stratification and wind flow in complex terrain violate the homogeneity assumption of the most of the cases , thus often deviating from a logarithmic wind profile

Stable stratification -  The anisotropy parameter seems relatively constant with height for neutral and stable conditions, whereas turbulence seems more isotropic for unstable stratification. This tendency is expected because turbulence in the bulk of the convective boundary layer under weak wind conditions is relatively isotropic. Close to the surface the shear, which maintains the anisotropy, is strong regardless of stability, so here anisotropic parameter varies much less with stability than further away from the surface. The profiles of length‐scale  are in agreement with the expected behaviour with stability of the length‐scale of the wind profile, which predicts larger length‐scales in unstable compared to stable conditions with a neutral length‐scale profile in between. Further, the size of the convective eddies is largest in unstable conditions, as expected.

Wind flow in complex terrain - The surface roughness length describes the roughness characteristics of the terrain. It is formally the height at which the wind speed becomes zero when the logarithmic wind profi le is extrapolated to zero wind speed. A corresponding system uses roughness classes.In offshore conditions the roughness length varies with the wave condition, which in turn is a function of wind speed, wind direction, fetch, wave heights and length.Over hill or mountain tops the flow will be generally accelerated. As a consequence the logarithmic wind profi le will be distorted: both steeper and then less steep depending on height. The degree of distortion depends on the steepness of the terrain, on the surface roughness and the stability. In very steep terrain the fl ow across the terrain might become detached and form a zone of turbulent separation. As a rule of thumb this phenomena is likely to happen in terrain steeper than 30% corresponding to a 17° slope. The location and dimensions of the separation zone depend on the slope and its curvature as well as roughness and stability. In cases of separation, the wind speed profi le might show areas with negative vertical gradient, where the wind speed is decreasing with height.