Characteristics of the Wind - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 491

to sunset, dissolution of the convective boundary layer begins abruptly, and the heal flux
over the entire layer turns negative within minutes. With the surface temperatures dropping
rapidly after sunset, an inversion layer often develops near the ground. This nocturnal
boundary layer continues to deepen throughout the evening, reaching a few hundred meters
in thickness about six hours after sunset. The atmosphere becomes stable and remains so
until sunrise.
It is important to note that on cloudy or windy days, neutral or near-neutral conditions
may prevail throughout the entire day. Neutral conditions are also observed to prevail at
high wind speeds and during heavy cloud cover.

Empirical Equations for the Atmospheric Stability Function

The influence of atmospheric stability on the wind speed profile is given in the
logarithmic/linear law by the term y s , which is a function of the ratio of the elevation to
the Monin-Obukhov stability length , or z / L s . The stability length L s is a measure of the ratio
of mechanical shear forces to the thermal buoyant forces causing atmospheric motion
[Mikhail 1984]. It is difficult to predict L s quantitatively, so we will treat it as an empirical
constant in the same way as z 0 . The different functions reported in the literature for y s can
be simplified for engineering purposes to the following:

Neutral atmosphere : y s = 0 (8-10c)

Stable atmosphere : y

s = +4.5 z / L s

, z £ L s (8-10d)

y

s = + 4.5[1 + ln( z / L )]

, z > L s (8-10e)

Unstable atmosphere : y

s = -0.5 z / L s

, z £ L s (8-10f )

y

s = -0.5[1 + ln( z / L s )] , z > L s

(8-10g)

Equations (8-10e and -l0g) effectively uncouple the wind shear at elevations above L s from
z 0 and extend the logarithmic/linear gradient at L s to higher elevations. In the terminology
of atmospheric science, L s is negative for an unstable atmosphere, but this is not significant
here since we are using it as an empirical constant.
Figure 8-12 illustrates the application of Equations (8-10). The test data in this figure
are the average and range of steady wind speeds measured at 15 elevations above flat,
homogeneous terrain at 0500 and 1200 hours on 16 consecutive days [Sisterson and Frenzen
1978]. At noon (Fig. 8-12(a)) the atmosphere is well-mixed and neutral or near-neutral, so
y s is zero. Fitting a straight line to the average wind speed data produces a value of 0.025
for z o . At the reference elevation of 10 m, the reference wind speed is 3.5 m/s (by
interpolation), and the coefficient U * / k is calculated to be equal to 0.58 m/s.
Figure 8-12(b) shows the increased wind shear and an uncoupled high-level jet that can
occur under stable atmospheric conditions during the early morning hours. At an elevation
of 10 m the reference wind speed is 2.1 m/s. The curve-fit parameters for this condition
are 15 m for L s and 0.25 m/s for U * / k . In accordance with Equation 8-10e, the extended
logarithmic/linear line above L s is tangent to the curve of the data at z = L s , and its slope
is 5.5 times the slope at z = z o . This linear extension also indicates the uncoupled nature
of the jet centered at an elevation of approximately 150 m.