F ¼ qwk þ qwk 0 þ qw 0 k þ qw 0 k 0 þ q 0 Wk þ q 0 Wk 0 þ q 0 w 0 k þ q 0 w 0 k 0
ð3:19Þ
In the last equation, the mean fluctuations, by definition, equal to zero. Fluctuations of q are also zero because the fluid does not vary in density and is
incompressible. The average value of w is likewise zero.
Thus, Eq. (3.19) can be simplified:
F ¼ q w 0 k 0
ð3:20Þ
Equation (3.20) applied to various momentum fluxes, sensible heat, latent heat,
and carbon dioxide, is given by
s ¼ À qu 0 w 0
ð3:21Þ
H ¼ q c p w 0 T 0
ð3:22Þ
LE ¼ q Lw 0 q 0
ð3:23Þ
C ¼ q w 0 c 0
ð3:24Þ
Combining Eq. (2.10) s ¼ qu
2
à from Chap. 2, with Eq. (3.21) we have
s ¼ Àqu 0
1 u 0
3
which gives the defining equality of friction velocity u
2
Ã
u
2
à ¼ Àu 0
1 u 0
3
ð3:25Þ
To measure fluctuations described in these equations, sensitive instrumentation
coupled to a data acquisition system is needed. Sensors need to be synchronized
and should be of sufficiently high frequency to record fluctuations of the properties
of smaller eddies capable of turbulent transport. For example, in forested areas,
aerodynamic studies require sensors capable of operating between 0.1 and 10 Hz.
3.3 Taylor’s Hypothesis
This hypothesis can be used mainly to replace analysis of micrometeorological
parameters in a large region of space region at an instant in time, with analysis of a
single point in space, over an extended period. This is the basis for installing
observation towers, at a given point on terrain, equipped with appropriate instrumentation to characterize microclimates and for the measurement of vertical fluxes
of energy and mass. Taylor’s hypothesis assumes that for a given property U, a
38
3 Characterization of Turbulent Flow in the Surface Boundary Layer
ð3:19Þ
In the last equation, the mean fluctuations, by definition, equal to zero. Fluctuations of q are also zero because the fluid does not vary in density and is
incompressible. The average value of w is likewise zero.
Thus, Eq. (3.19) can be simplified:
F ¼ q w 0 k 0
ð3:20Þ
Equation (3.20) applied to various momentum fluxes, sensible heat, latent heat,
and carbon dioxide, is given by
s ¼ À qu 0 w 0
ð3:21Þ
H ¼ q c p w 0 T 0
ð3:22Þ
LE ¼ q Lw 0 q 0
ð3:23Þ
C ¼ q w 0 c 0
ð3:24Þ
Combining Eq. (2.10) s ¼ qu
2
à from Chap. 2, with Eq. (3.21) we have
s ¼ Àqu 0
1 u 0
3
which gives the defining equality of friction velocity u
2
Ã
u
2
à ¼ Àu 0
1 u 0
3
ð3:25Þ
To measure fluctuations described in these equations, sensitive instrumentation
coupled to a data acquisition system is needed. Sensors need to be synchronized
and should be of sufficiently high frequency to record fluctuations of the properties
of smaller eddies capable of turbulent transport. For example, in forested areas,
aerodynamic studies require sensors capable of operating between 0.1 and 10 Hz.
3.3 Taylor’s Hypothesis
This hypothesis can be used mainly to replace analysis of micrometeorological
parameters in a large region of space region at an instant in time, with analysis of a
single point in space, over an extended period. This is the basis for installing
observation towers, at a given point on terrain, equipped with appropriate instrumentation to characterize microclimates and for the measurement of vertical fluxes
of energy and mass. Taylor’s hypothesis assumes that for a given property U, a
38
3 Characterization of Turbulent Flow in the Surface Boundary Layer