u 0
n u 0
n
u 0
n v 0
n
u 0
n w 0
n
v 0
n u 0
n
v 0
n v 0
n
v 0
n w 0
n
w 0
n u 0
n
w 0
n v 0
n
w 0
n w 0
n
2
6
4
3
7
5
ð3:188Þ
A third rotation can be applied around the x-axis to cancel out the lateral
momentum v 0 w 0 . This rotation is nil in flat or slightly sloped surfaces.
(vi) The vertical turbulent flux of a quantity, F ¼ w 0 k 0 , from Eqs. (3.165) to
(3.168) is given by a general expression:
F ¼ w 0 k 0 ¼ ðw À wÞðk À kÞ
ð 3:189Þ
Determining the means involves direct calculation of means, filtering, and
removing linear trends (Aubinet et al. 2000). After data acquisition, the means of x i
are given by the statistical definition:
x i ¼
P n
i¼1
x i
n
ð3:190Þ
and the mean of the covariances is given by
x 0 y 0 ¼
1
n
X n
k¼1
x 0
k y 0
k
ð3:191Þ
Another alternative for data processing in real time is to use the running mean.
Under these conditions, the running mean x i , is given by
x i ¼ a n x iÀ1 þ 1 À a n
ð
Þx i
ð3:192Þ
where a n is the weighting factor given by
a n ¼ exp ÀDt=s s
ð
Þ
ð3:193Þ
In Eq. (3.193), Dt is the time interval between measurements, for example, 0.1 s.
The values for s s (time constant) proposed vary between 200 s. and 20 min.
If Dt/s s << 1, then Eq. (3.193) can be written as
a n ¼ 1 À Dt=s s
ð
Þ
ð3:194Þ
For removing linear trends, the mean x k is calculated as
x k ¼ x þ b ðt k À
1
n
X n
1
t k Þ
ð 3:195Þ
88
3 Characterization of Turbulent Flow in the Surface Boundary Layer
n u 0
n
u 0
n v 0
n
u 0
n w 0
n
v 0
n u 0
n
v 0
n v 0
n
v 0
n w 0
n
w 0
n u 0
n
w 0
n v 0
n
w 0
n w 0
n
2
6
4
3
7
5
ð3:188Þ
A third rotation can be applied around the x-axis to cancel out the lateral
momentum v 0 w 0 . This rotation is nil in flat or slightly sloped surfaces.
(vi) The vertical turbulent flux of a quantity, F ¼ w 0 k 0 , from Eqs. (3.165) to
(3.168) is given by a general expression:
F ¼ w 0 k 0 ¼ ðw À wÞðk À kÞ
ð 3:189Þ
Determining the means involves direct calculation of means, filtering, and
removing linear trends (Aubinet et al. 2000). After data acquisition, the means of x i
are given by the statistical definition:
x i ¼
P n
i¼1
x i
n
ð3:190Þ
and the mean of the covariances is given by
x 0 y 0 ¼
1
n
X n
k¼1
x 0
k y 0
k
ð3:191Þ
Another alternative for data processing in real time is to use the running mean.
Under these conditions, the running mean x i , is given by
x i ¼ a n x iÀ1 þ 1 À a n
ð
Þx i
ð3:192Þ
where a n is the weighting factor given by
a n ¼ exp ÀDt=s s
ð
Þ
ð3:193Þ
In Eq. (3.193), Dt is the time interval between measurements, for example, 0.1 s.
The values for s s (time constant) proposed vary between 200 s. and 20 min.
If Dt/s s << 1, then Eq. (3.193) can be written as
a n ¼ 1 À Dt=s s
ð
Þ
ð3:194Þ
For removing linear trends, the mean x k is calculated as
x k ¼ x þ b ðt k À
1
n
X n
1
t k Þ
ð 3:195Þ
88
3 Characterization of Turbulent Flow in the Surface Boundary Layer