Gasch R., Twele J. (Eds.) Wind Power Plants: Fundamentals, Design, Construction and Operation

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4.2 Atmospheric boundary layer

122

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Wind speed v

in m/s

Height z in m

1,00

0,10

0,01

0,005

Roughness length z

in m

Forest

Bushy farm land

Pasture, grass

Calm sea, sands

Assumption:

same v

= 15 m/s

at height z = 1000 m

1,00

0,005

Fig. 4-7 Vertical wind profile for different roughness lengths z

, assumed “geostrophic wind” of

15 m/s

The graphical interpretation of this equation (i.e. the intercept theorems) is shown

in Fig. 4-8. The line drawn through the two measuring points hits the horizontal

logarithmic axis (ln z) exactly where the wind speed is zero. So Fig. 4-8 also

shows the physical meaning of the roughness length, it is the height above ground

where in the mean the wind speed is zero. In Fig. 4-7 the starting points of the

wind profile curves at v = 0 m/s with the individual z

values are subvisible; the

vertical axis resolution is not fine enough.

If this procedure for the determination of the roughness length is applied, the

height differences of the two anemometers must be sufficiently large, e.g. using

the heights above ground of 20 m and 40 m [38]. Often the measuring mast is

equipped with three or four anemometers with measuring heights up to 80 m.

Then there are more points for fitting the interpolated line in Fig. 4-8.

In wind farm planning, the roughness length has to be estimated for a large area

of up to several square kilometres since changes of the roughness length in the

surrounding area, Fig. 4-9, have an influence on the vertical wind profile over a

larger distance. These large-scale considerations for estimation of the roughness

are based on the topography descriptions (site inspections, mappings, satellite im-

ages).

Offshore, the surface roughness is determined by the actual swell. Depending

on the wind speed, the exposure time and the wind direction the swell develops

characteristic wave heights and lengths which determine the roughness of the

ocean surface. Recent investigations [15] indicate that offshore the wind profile is

significantly influenced by the atmospheric stratification since the surface rough-

ness is generally very small.

4 The wind

123

Fig. 4-8 Determination of roughness length z

from measurements at two different heights z

and

Fig. 4-9 Influence of roughness change on the vertical wind profile – transition zone

-20246

ln z

4.2 Atmospheric boundary layer

124

As mentioned, the above equations (4.1) to (4.4) are only valid for a neutrally

stable atmosphere, an idealized absolutely flat surface with a uniform roughness

length. A different temperature profile causes changes in the vertical heat and

mass transfer which create differences in the turbulence, the wind profile and

therefore the wind speed gradient.

The extended description of the vertical wind profile adds to the logarithmic wind

profile a correction term which considers the atmospheric stratification due to the

vertical temperature profile:

<

)(

. (4.5)

The empirical stability function

takes into account the influence of the thermal

stratification; it is positive for an unstable and negative for a stable atmosphere,

and surely zero for a neutrally stable atmosphere.

The so-called Monin-Obukhov stability length L (its dimension is meter) is the

parameter which describes the vertical mass exchange due to the ratio of friction

forces and lift forces [31]. From measurements the Monin-Obukhov stability

length can be determined directly or indirectly. A direct measurement is possible

e.g. with an ultrasonic anemometer (cf. section 4.3.2) or by measuring the tem-

perature difference of the air in two heights. For a first estimation, tables on the

Monin-Obukhov stability length in dependence of the roughness length z

and the

atmospheric stability are useful, e.g. in the German Technical Instructions on Air

Quality (TA-Luft, dated 2002) [32].

Fig. 4-10 shows the already mentioned influence of the atmospheric stratifica-

tion on the wind profile. The wind profiles are normalized for the measuring

height of 30 m.

The logarithmic wind profile is valid for the infinitely flat and even terrain. But

in reality, there may be considerable effects of the surface contour (i.e. the topo-

graphy) on the wind profile and also on the wind speeds occurring in the rotor area

of the wind turbine. The possibilities to describe these effects using fluid mechan-

ics approaches are quite limited. Especially for complex and steep terrain as well

as for strong atmospheric stratification the wind profiles obtained by extensive

efforts in numerical simulation are still unsatisfactory.

4 The wind

125

Fig. 4-10 Vertical wind profile – influence of atmospheric stability [1]

Surface formations lead to a deformation of the vertical wind profile. In general,

the wind speed is accelerated when flowing over the top of hills and mountains,

Fig. 4-11. The wind profile gets steeper. The wind profile shape on the summit

depends on the surface roughness of the terrain. If the slope is very steep, with an

inclination of more than 30%, flow separation occurs on the leeward side. Inside

the turbulent separation bubble the wind is very intermittent. The size of the sepa-

ration bubble depends on the inclination and the curvature of the elevation, the

temperature profile and also on the surface roughness. In extreme cases there may

be a decrease of the wind speed with height above ground.

4.2 Atmospheric boundary layer

126

Turbulent

separation

Steep slope

Gentle slope

Fig. 4-11 Influence of topography and roughness on the vertical wind profile [9]

The wind speed is not only influenced by terrain structure and surface type but

also by obstacles like e.g. houses and forests. Fig. 4-12 shows the relative reduc-

tion of the wind speed in the shade behind a two-dimensional structure. In the

hatched area, the shading strongly depends on the detailed geometry of the obstacle.

Fig. 4-12 Relative reduction of wind speed behind obstacles [5]

4 The wind

127

Above the surface boundary layer (Prandtl layer), there is the Ekman layer. Here,

the wind profile is additionally influenced by the Coriolis force. This effect is con-

sidered by the following analytic expression [16] for the wind profile



z2ȖzȖ

cos)21()(



 ezeuzv

(4.6)

where u

is the absolute value of the geostrophic wind and Ȗ is the coefficient

which describes the vertical turbulent mass transfer. It is assumed that it is con-

stant, but its value is depending on the surface roughness and the atmospheric

stratification and may be estimated only from measurements. Thus, there is also in

equation (4.6) an uncertainty concerning the calculated vertical wind profile. But

for large heights above ground it is more suitable than equation (4.5).

4.2.3 Turbulence intensity

The fluctuations of the wind speed in the atmosphere belong to processes with a

time scale from less than one second to several days and a spatial structure from

some millimetres to several kilometres, Fig.s 4-13 and 4-23.

Fig. 4-13 Spatial and temporal scale of atmospheric phenomena [16]

4.2 Atmospheric boundary layer

128

The diurnal, synoptic and seasonal fluctuations of the wind are used together with

the mean wind speed to predict the energy yield for a site, on one hand. On the

other, the knowledge about turbulence and gustiness is required first of all for the

load calculation of the wind turbine.

The fluctuating wind is described (roughly) by the mean wind speed

v in the con-

sidered time period (mostly 10 min) and the turbulence intensity I

, Fig. 4-14.

Fig. 4-14 Turbulent wind and mean wind speed v

The mean wind speed in the measuring period T is

)(

dttv

v . (4.7)

The average of the squared difference of the actual value to the mean wind speed

is the variance, a measure for the “irregularity” of the wind





)(

dtvtv

v . (4.8)

The square root of the variance is the standard deviation,

, which has

the same dimension as the mean wind speed

. The ratio of standard deviation to

the mean wind speed gives the turbulence intensity I

0 50 100 150 200 250 300

Zeit in s

Windgeschwindigkeit v in m/s

= 7,5 m/s

= 16 %

Time t in s

Wind speed v in m/ s

v(t)

0 50 100 150 200 250 300

Zeit in s

Windgeschwindigkeit v in m/s

= 7,5 m/s

= 16 %

Time t in s

Wind speed v in m/ s

v(t)

4 The wind

129

. (4.9)

Roughly considered, the turbulent fluctuations have a Gaussian distribution

around the mean value

v with the standard deviation V

, cf. Fig. 4-30. But cer-

tainly extreme gusts like the 50-year extreme wind speed (see chapter 9, table 9.2)

are not included in this range.

The turbulence intensity varies in a large range from I

= 0.05 to 0.40 due to

the natural fluctuations but also due to different averaging periods of the meas-

urements and optionally the time response of the sensors.

There are two fundamental types of atmospheric turbulence: mechanical turbu-

lence and thermally induced turbulence. Mechanical turbulence comes from the

shear in the wind profile. It depends on wind flow from the large-scale pressure

gradients and on the surface roughness. This share of the turbulence intensity is

estimated based on fluid mechanics for a neutrally stable atmosphere in flat terrain

with

ln/1

. (4.10)

Thermal turbulence is caused by heat convection and depends first of all on the

temperature difference between the ground and the air masses above it.

Measurements show that the turbulence intensity decreases with increasing

wind speed, Fig. 4-15. At low wind speeds, the turbulence intensity strongly de-

pends on the atmospheric stability.

Above the ocean surface, these facts are no longer valid, since here the wind

flow creates the roughness by itself since it forms the waves. The formation of the

roughness is influenced not only by the actual wind speed, Fig. 4-16, but also by

the time of action on the ocean surface meaning that the roughness is time-

dependent. In general, the roughness increases, like the wave height, with higher

wind speeds.

4.2 Atmospheric boundary layer

130

Fig. 4-15 Turbulence intensity versus wind speed, example of an onshore measurement

Fig. 4-16 Turbulence intensity versus wind speed, example of an offshore measurement at two

different heights [26]

4 The wind

131

4.2.4 Representation of measured wind speeds in the time domain

by frequency distribution and distribution functions

The determination of the annual energy yield and as well the assessment of the

wind turbine loads are mostly based on measured 10-min averages of the wind

speed; seldom is the averaging period a 1-min or 1-hour interval.

Additionally, the wind direction is measured during the whole measuring

period using a wind vane, and all the values are recorded in time series.

Apart from the 10-min average wind speed, the maximum and minimum value

as well as the standard deviation of the averaging period may be stored in the data

series as well, cf. Fig. 4-30.

The measuring period should be long enough, especially for the calculation of

the predicted energy yield at a site. Depending on the local climate, the wind

speed may undergo strong seasonal fluctuations, so the measuring period should

be an integer multiple of a year.

Investigations show that the annual energy content of the wind may vary in a

range of up to

r25% [5]. Fig. 4-17 shows for a period of 100 years the energy con-

tent averaged over five-year periods and normalized with the 100-year average.

The strong fluctuations are clearly visible.

On one hand, the long-term measuring data should be stored carefully, (“at best

on a CD ROM in a safe”). On the other, it has to be processed using statistics.

Fig. 4-17 Relative wind energy, averages over 5-year periods in Laeso, DK [5]