High Meteorology: Wind throughout the boundarylayer

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High Meteorology Wind throughout the
boundary-layer

• Sven-Erik Gryning, Hans E Jørgensen, Poul Astrup,
  Lars Landberg
• Wind Energy Department
• Risø National Laboratory, Denmark
• Lars.Landberg_at_risoe.dk

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Wind profiles over flat homogeneous terrainMap
of the Høvsøre site at the west coast of Jutland
with measuring sector shown
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30 degrees 60 degrees 90
degrees views from the mast
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Measured wind profiles, sector 30 to 90 deg.
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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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Monin-Obukhov wind profilesplanetary boundary
layer only, constant flux and based on Businger
(-1/4 power)
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but for unstable conditions
actually, the theoretically correct correction
for convective conditions reads
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Monin-Obukhov wind profilesplanetary boundary
layer only, constant flux and based on
convective scaling (-1/3 power)
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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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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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Length scales
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In the atmospheric surface layer (not influenced
by and ) the above expression
reduces to the logarithmic wind profile  
  and in the lower part of the boundary layer
(not influenced by )  
  and for the entire boundary layer  
Neutral
 
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Stability correctionThe 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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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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Monin-Obukhov wind profilesplanetary boundary
layer only, constant flux and based onconvective
scaling (-1/3 power)and constant length scale in
the middle layer
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Conclusion the wind profile in the lower part of
the boundary-layer over homogeneous terrain in
near neutral conditions
 

  Both expressions reduces for neutral condtions,
to  
   
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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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Unstable conditions (daytime)
Profiles of momentum (far left) and kinematic
heat flux (less left), to determine the
boundary layer height
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Boundary layer height estimated from the measured
profiles of momentum and kinematic heat fluxes.
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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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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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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.