Environmental Engineering Reference
In-Depth Information
it may be at virtually ground level, meaning the wind resource varies scarcely at all
across the site. In complex terrain and with mixed land cover, the convergence height
might be several hundred to thousands of meters above the mean ground elevation.
What is most useful about the convergence height is its corollary: near the ground,
wind shear tends to be inversely related to mean speed. This is because the greater
the shear is, the more rapidly the speed decreases from the convergence height down
to the surface, and therefore, the lower the speed at the height of measurement. (This
is implied in Figure 10-1 if one imagines the convergence height is 120 m.)
The presumed inverse relationship between wind shear and speed occurs only if
the shear is fairly constant with height, or at least varies with height in a similar way
across the project area. This, as we have seen, does not always hold true. Nevertheless,
such a relationship is observed surprisingly often and can be used as a tool to inform
judgments about the likely change in shear above a particular mast.
For example, suppose a mast exhibits both a high shear and a high mean speed
relative to other masts in the project area. It is reasonable to conclude that this shear
cannot persist to a great height, as otherwise the speed profile above the mast would
diverge from the others. Likewise, a mast with a relatively low speed and low shear
can be expected to see an increase in shear with height. A simple scatter plot of
shear exponent versus mean speed can be used to identify towers that deserve closer
examination (note that the speeds and shears should be for the same heights and
time periods). Any outliers should first be examined for poor data quality, incorrect
instrument heights, or other problems that could account for the apparent discrepancy.
If no such errors are found, the shear exponents for the outlying towers can be adjusted
to avoid unrealistic divergence in the speed profiles. The approach is illustrated in
Figure 11-2, which is taken from a wind project site in the United States. In this case,
the shear at the outlying point circled in red was adjusted downward.
11.1.4 Logarithmic Method
The most commonly used logarithmic expression for wind shear is the following
equation:
log
h
2
/
z
0
log
h
1
/
z
0
v
2
=
v
1
(11.5)
Here,
z
0
is the surface roughness length, a parameter linked to the height and density
of vegetation and other rough elements surrounding the tower. Strictly speaking, this
equation is applicable only when the boundary layer is neutrally buoyant.
2
At times
2
Buoyancy is defined in terms of the adiabatic rate of temperature change with height. This is the rate of
change in temperature of a parcel of air that is displaced upward or downward, only due to its change in
pressure, with no exchange of heat with the surrounding air. If the actual temperature lapse rate exceeds this
critical rate then a parcel of air displaced upward will find itself cooler and heavier than the surrounding air
and so will tend to sink back down: it is negatively buoyant or thermally stable. Conversely, if the lapse rate
is lower than the critical rate, the atmosphere is said to be thermally unstable and convective mixing results.
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