Vertical Profiles Over Flat Terrain - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 29

Relating the standard deviations to the mean wind speed rather than to the
friction velocity leads to the definition of turbulence intensity. The streamwise
turbulence intensity is defined in equation (A.6) in Appendix A. By inserting the
leftmost relation from ( 3.9 ) into ( 3.6 ) we get for this turbulence intensity (Wie-
ringa 1973 ):

I u ð z Þ¼ r u

1
ln ð z = z 0 Þ

u ð z Þ ¼

ð 3 : 10 Þ

This means that turbulence intensity in the neutrally-stratified surface layer is a
function of surface roughness only. Increasing roughness lengths will lead to
higher turbulence intensities. For a given roughness length, turbulence intensity
decreases with height in the surface layer.

3.1.1.2 Unstable Stratification

The thermal stratification of the surface layer is rarely found to be abs olutel y
neutral. In most cases, there is a non-vanishing virtual potential heat flux H 0 v w 0 at
the ground [see the definition of potential temperature in Eq. ( 3.8 ), the virtual
potential temperature, H v includes the modifying influence of the atmospheric
humidity on the static stability of the air, see ( 2.14 )], which leads to a thermal
stratification of the surface layer. From this surface heat flux and the friction
velocity u * a length scale, L * , the Obukhov length (sometimes also called Monin-
Obukhov length, but the first term is historically more correct and will be used
here) can be formed:

u 3
H 0 v w 0

L ¼ H v
jg

ð 3 : 11 Þ

The heat flux is counted positive if it is directed from the atmosphere towards
the ground (cooling the atmosphere) and negative if it is towards the atmosphere
(heating the atmosphere). Thus an unstable surface layer is c haracterized by a
negative Obukhov length. The virtual potential heat flux H 0 v w 0 can be separated

into a sensible heat flux and a humidity flux:

H 0 v w 0 ¼ H 0 w 0 þ 0 : 61Hq 0 w 0 ð 3 : 12 Þ

The ratio of the turbulent sensible heat flux and humidity flux is called Bowen
ratio, B:

B ¼ c p H 0 w 0
L v q 0 w 0

ð 3 : 13 Þ

where q is specific humidity and L v is the (latent) heat of vaporisation. The
buoyancy

exerted by the vertical heat and humidity gradients is given by