Environmental Engineering Reference
In-Depth Information
account the DR in each month) is 7.49 m/s. However, the annualized average is only
7.39 m/s because the repeated months are windier, on average, than the other months.
Naturally, this method only works if the data record spans at least 12 months;
although if it is only 1 or 2 months short of 12, an approximate annualized mean can
sometimes be obtained by assuming that the missing months are similar to the months
immediately before and after. The method can be applied to other parameters such as
shear in a similar way.
10.1.3 Wind Shear
The wind shear (the rate of change in horizontal wind speed with height) is typically
expressed as a dimensionless power law exponent known as
alpha
(
). The power
law equation relates the wind speeds at two different heights in the following manner:
α
h
2
h
1
α
v
2
v
1
=
(10.5)
where
v
2
=
the wind speed at height
h
2
;
v
1
=
the wind speed at height
h
1
.
This equation can be inverted to define
α
in terms of the measured mean speeds and
heights:
log
v
2
v
1
α
=
log
h
2
h
1
(10.6)
Figure 10-2 depicts wind speed profiles for a range of exponents assuming a speed of
8.5 m/s at 120 m height.
Taking the average of the speeds before calculating the shear, as in the equation
above, conveniently yields a time-averaged shear exponent, which is of most interest
at this stage of the analysis. Time-averaged exponents can range from less than 0.10 to
more than 0.40, depending on land cover, topography, time of day, and other factors.
For short periods, and especially in light, unsteady winds, shear exponents can extend
well beyond this range. Typical mean shear values are shown in Table 10-3 for a
range of site conditions (this table is reproduced from Chapter 3). All other things
being equal, taller vegetation and obstacles lead to greater shear. Complex terrain also
usually produces greater shear, except on exposed ridges and mountain tops where
topographically driven acceleration can reduce shear. Sites in tropical climates tend to
have lower shear than similar sites in temperate climates because the atmosphere is less
often thermally stable. (The effect of thermal stability is discussed in the next chapter.)
The calculated shear is sensitive to small errors in the relative speed between the
two heights, and this sensitivity increases as the ratio of the two heights,
h
1
and
h
2
,
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