Page 45 - Wind Energy Handbook

TURBULENCE 19

loadings due to high wind shear. There can also be rapid changes in wind direction
with height in this situation.
In the following sections, a series of relationships are presented which describe
the properties of the atmospheric boundary layer, such as turbulence intensities,
spectra, length scales and coherence functions. These relationships are partly based
on theoretical considerations, and partly on empirical fits to a wide range of
observations from many researchers taken in various conditions and in various
locations.
In the neutral atmosphere, the boundary-layer properties depend mainly on the
surface roughness and the Coriolis effect. The surface roughness is characterized by
the roughness length z o . Typical values of z o are shown in Table 2.1.
The Coriolis parameter f is defined as

f ¼ 2Ù sin(jºj) (2:7)

where Ù is the angular velocity of the earth’s rotation, and º is the latitude. This is
zero at the equator, so the following description applies only to temperate latitudes.
Here the height of the boundary layer is given by

h ¼ u =(6 f ) (2:8)

where u is known as the friction velocity, given by:

u =U(z) ¼ k=[ln(z=z o ) þ Ø] (2:9)

where k is the von Karman constant (approximately 0.4), z is the height above
ground and z o is the surface roughness length. Ø is a function which depends on
stability: it is negative for unstable conditions, giving rise to low wind shear, and
positive for stable conditions, giving high wind shear. For neutral conditions, ESDU

(1985) gives Ø ¼ 34:5fz=u , which is small compared to ln(z=z o ) for situations of
interest here. If Ø is ignored, the wind shear is then given by a logarithmic wind
profile:

U(z) / ln(z=z o ) (2:10)

Table 2.1 Typical Surface Roughness Lengths
Type of terrain Roughness length z o (m)
Cities, forests 0.7
Suburbs, wooded countryside 0.3
Villages, countryside with trees and hedges 0.1
Open farmland, few trees and buildings 0.03
Flat grassy plains 0.01
Flat desert, rough sea 0.001