1. High Meteorology: Wind throughout the boundary-layer
Sven-Erik Gryning, Hans E Jørgensen, Poul Astrup, Lars Landberg
Wind Energy Department
Risø National Laboratory, Denmark

2. Wind profiles over flat homogeneous terrain Map of the Høvsøre site at the west coast of Jutland with measuring sector shown
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3. 30 degrees
60 degrees
90 degrees
views from the mast
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4. Measured wind profiles, sector 30 to 90 deg.
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5. Commonly used expression for the wind profile
Neutral atmosphere
Stable atmosphere (nighttime)
Unstable atmosphere (daytime) .
with the standard stability correction (Businger)
based on measuremets at small masts (Kansas experiment):
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6. Monin-Obukhov wind profiles planetary boundary layer only, constant flux and based on Businger (-1/4 power)
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7. but for unstable conditions
actually, the theoretically correct correction for convective conditions reads:
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8. Monin-Obukhov wind profiles planetary boundary layer only, constant flux and based on
convective scaling (-1/3 power)
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9. Wind profile, common knowledge
The wind profile for the boundary layer can be expressed as:
where is the local friction velocity (proportional to the square root of the local Reynolds stress). The length scale is denoted it is a function of the state of the atmosphere and height
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10. Length scales
The behaviour of the length scale is modelled by inverse summation of the three terms .
which can be written .
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11. Length scales
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12. and in the lower part of the boundary layer (not influenced by )
In the atmospheric surface layer (not influenced by and ) the above expression reduces to the logarithmic wind profile:
surface layer
and in the lower part of the boundary layer (not influenced by )
lower part of the boundary layer
and for the entire boundary layer  
Neutral
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13. neglecting the (unknown) stability dependence on and
Stability correction The effect of atmospheric stability will be derived as a correction to the wind profile in neutral conditions.
neglecting the (unknown) stability dependence on and
For atmospheric stable conditions, Businger et al. (1971)
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14. Wind profile - unstable
For atmospheric unstable conditions ( negative )
where Businger et al. (1971) suggested and   and the theoretical correct value for convective conditions is p= -1/3 and a= -12.
Then the length scale can be expressed as:
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15. Monin-Obukhov wind profiles planetary boundary layer only, constant flux and based on convective scaling (-1/3 power) and constant length scale in the middle layer
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16. Both expressions reduces for neutral condtions, to
Conclusion: the wind profile in the lower part of the boundary-layer over homogeneous terrain in near neutral conditions
for
for
Both expressions reduces for neutral condtions, to
LMBL(m) 22
107
329
neutral
-342
-148
-72
L (m) ∞
300
160
400
800
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17. Profiles of momentum (left)
and kinematic heat flux (below), to determine the boundary layer height
Stable conditions
(nighttime, sometimes
daytime winter)
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18. Unstable conditions (daytime)
Profiles of momentum (far left)
and kinematic heat flux (less left),
to determine the boundary layer
height
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19. Boundary layer height estimated from the measured profiles of momentum and kinematic heat fluxes.
Momentum flux profile
Kinematic heat flux profile
Monin-Obukhov length, L (m)
Exp
(m)
Eq. (X)
Power
Mean 25
215
270
138
161
190 97
202
258
154
184
362
192
252
210
282
240
Neutral
289
418
300
-280
653
1676
246
312
500
-139
387
734
299
521
-75
489
1033
267
423
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20. Which one is the better? It is clear that the height of the
boundary layer is important for the
stable cases where the height is about
200 metres.
But it is not clear how to parameterize
the length scale close to its top.
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21. Conclusions on wind profiles
Above the surface boundary layer the neutral wind profile deviates from logarithmic. It can be argued to be caused by the length scale not
being proportional to height (as in the surface layer) but approaching a
constant value.
Under very convective conditions use of a formulation for the stability correction that fulfills the theoretical requirements for the convective limit is seen to perform better than the commonly used Businger formulation.
Inclusion of the boundary layer height improves the wind profile, the effect was clearly seen during atmospheric the stable conditions where the boundary layer height was only slightly higher than the maximum measuring height. The effect is less well seen during unstable and neutral conditions where the boundary layer height is much higher than he measuring height.
The behaviour of the length scale near the top of the boundary layer is not clear.
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22. Conclusions on measurements
The measurements at 160 meters height were of decisive importance for the interpretation of the wind profiles. A 200 metre mast seems appropiate and wishful thinking for the national test station for large wind turbines
Measurements of the height of the boundary-layer are missing and should be added. Research on how to achieve this parameter should be initiated.
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