Page 46 - Wind Energy Handbook

20 THE WIND RESOURCE

A power law approximation,

U(z) / z Æ (2:11)

is often used, where the exponent Æ is typically about 0.14, but varies with the type
of terrain. However, the value of Æ should also depend on the height interval over
which the expression is applied, making this approximation less useful than the
logarithmic profile.
If the surface roughness changes, the wind shear profile changes gradually
downwind of the transition, from the original to the new profile. Essentially, a new
boundary layer starts, and the boundary between the new and old boundary layers
increases from zero at the transition point until the new boundary layer is fully
established. The calculation of wind shear in the transition zone is covered by, for
example, Cook (1985).
By combining Equations (2.8) and (2.9), we obtain the wind speed at the top of
the boundary layer as
! !

u u
U(h) ¼ ln ln 6 þ 5:75 (2:12)
k fz 0

This is similar to the so-called geostrophic wind speed, G, which is the notional
wind speed driving the boundary layer as calculated from the pressure field. The
geostrophic wind speed is given by

v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
"
#
!
u
u 2
u t u
G ¼ ln A þB 2 (2:13)
k fz 0
where, for neutral conditions, A ¼ ln 6 and B ¼ 4:5. This relationship is often
referred to as the geostrophic drag law.
The effect of surface roughness is not only to cause the wind speed to decrease
closer to the ground. There is also a change in direction between the ‘free’ pressure-
driven geostrophic wind and the wind close to the ground. Although the geo-
strophic wind is driven by the pressure gradients in the atmosphere, coriolis forces
act to force the wind to flow at right angles to the pressure gradient, causing a
characteristic circulating pattern. Thus in the northern hemisphere, wind flowing
from high pressure in the south to low pressure in the north will be forced
eastwards by coriolis effects, in effect to conserve angular momentum on the
rotating earth. The result is that the wind circulates anti-clockwise around low-
pressure areas and clockwise around high-pressure areas, or the other way round
in the southern hemisphere. Close to the ground, these flow directions are modified
due to the effect of surface friction. The total direction change, Æ, from the
geostrophic to the surface wind is given by