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@risoe.dk

Wind profiles over flat homogeneous terrain Map of the Høvsøre site at the west coast of Jutland with measuring sector shown EWEC 06, Athens

30 degrees 60 degrees 90 degrees views from the mast EWEC 06, Athens

Measured wind profiles, sector 30 to 90 deg. EWEC 06, Athens

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): EWEC 06, Athens

Monin-Obukhov wind profiles planetary boundary layer only, constant flux and based on Businger (-1/4 power) EWEC 06, Athens

but for unstable conditions actually, the theoretically correct correction for convective conditions reads: EWEC 06, Athens

Monin-Obukhov wind profiles planetary boundary layer only, constant flux and based on convective scaling (-1/3 power) EWEC 06, Athens

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 EWEC 06, Athens

Length scales   The behaviour of the length scale is modelled by inverse summation of the three terms . which can be written   . EWEC 06, Athens

Length scales EWEC 06, Athens

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 EWEC 06, Athens

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) EWEC 06, Athens

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:           EWEC 06, Athens

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 EWEC 06, Athens

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 EWEC 06, Athens

Profiles of momentum (left) and kinematic heat flux (below), to determine the boundary layer height Stable conditions (nighttime, sometimes daytime winter) EWEC 06, Athens

Unstable conditions (daytime) Profiles of momentum (far left) and kinematic heat flux (less left), to determine the boundary layer height EWEC 06, Athens

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 EWEC 06, Athens

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. EWEC 06, Athens

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. EWEC 06, Athens

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. EWEC 06, Athens