Statistical Tools - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 169

Fig. A.6 Typical example of
an autocorrelation function
from FINO1 data (Fig. 3.3
from Türk 2008 )

autocorrelation function has decreased to 1/e & 0.37. Multiplying the time scale
with the mean wind speed u gives the spatial dimension K u of this element in flow
direction und the assumption of the validity of Taylor's frozen turbulence
hypothesis. This spatial dimension is called integral turbulence length scale.
K u ¼ uT u ¼ u Z

1

R u 0 u 0 ð s Þ ds ð A : 41 Þ

0

Figure A.6 shows an example where the time scale is of the order of 50 s. As
the mean wind speed increases with height, this means that the integral turbulence
length scale according to ( A.40 ) increases with height as well.