Civil Engineering Reference
In-Depth Information
Figure 3.1
Wind speeds at three heights during
gales (Deacon, 1955).
3.2
Mean wind speed profiles
3.2.1
The 'logarithmic law'
In this section we will consider the variation of the mean or time-averaged wind speed
with height above the ground near the surface (in first 100-200 m—the height range of
most structures). In strong wind conditions, the most accurate mathematical expression is
the 'logarithmic law'. The logarithmic law was originally derived for the turbulent
boundary layer on a flat plate by Prandtl; however, it has been found to be valid in an
unmodified form in strong wind conditions in the atmospheric boundary layer near the
surface. It can be derived in a number of ways. The following derivation is the simplest
and is a form of dimensional analysis.
We postulate that the wind shear, i.e. the rate of change of mean wind speed,
Ū,
with
height, is a function of the following variables:
• the height above the ground,
z;
• the retarding force per unit area exerted by the ground surface on the flow—known as
the surface shear stress, τ
0
;
• the density of air,
ρ
a
.
Note that near the ground, the effect of the earth's rotation (Coriolis forces) is neglected.
Also because of the turbulent flow, the effect of molecular viscosity can be neglected.
Combining the wind shear with the above quantities, we can form a non-dimensional
wind shear:
