Wind shear/Log-law

Wind shear
Wind shear graph         The graph was plotted with the Wind Speed Calculator of this page. It shows how wind speeds vary in roughness class 2 (agricultural land with some houses and sheltering hedgerows with some 500 m intervals), if it is assumed that the wind is blowing at 10 m/s at a height of 100 m.
        The fact that the wind profile is twisted towards a lower speed when moving closer to ground level, is usually called wind shear. Wind shear may also be important when designing wind turbines. If a wind turbine is considered with a hub height of 40 m and a rotor diameter of 40 m, then the wind is blowing at 9.3 m/s when the tip of the blade is in its uppermost position and only 7.7 m/s when the tip is in the bottom position, because of the wind shear. This means that the forces acting on the rotor blade when it is in its top position are far larger than when it is in its bottom position.

Wind shear and escarpments
Escarpment and wind turbines        The aerial photograph shows a good site for wind turbines along a shoreline with the turbines standing on a cliff which is about 10 m tall. It is a common mistake to believe that in this case one may add the height of the cliff to the height of the wind turbine tower to obtain the effective height of the wind turbine, when one is doing wind speed calculations, at least when the wind is coming from the sea.
        This is patently wrong. The cliff in the front of the picture will create turbulence and brake the wind even before it reaches the cliff. It is therefore not a good idea to move the turbines closer to the cliff. That would most likely lower energy output and cause a lower lifetime for the turbines, due to more tear and wear from the turbulence.
        If there was a choice, it would be preferable to have a nicely rounded hill in the direction facing the sea, rather than the escarpment of the picture. In case of a rounded hill, there would be also a speed up effect.

        The most common mathematical model for accounting the variation of the horizontal wind speed with height is the log-law, which has its origin in boundary layer flow in fluid mechanics and in atmospheric research. It can be used until heights of about 150-200m without loss of accuracy. The log-law gives the wind speed at a specific height as a function of the terrain parameters.
        For a low roughness and homogeneous terrain, that is for open areas, the log-law gives:
                  u(z)=(u*/k)ln(z/z0)      for z>z0
where u(z) is the wind speed at height z, u* is the friction velocity and k is the Von Karman constant, taken as k=0.4.

Video frames
- Expressions for V(h): exponential law, logarithmic law

- Wind shear calculator