turbulent eddy does not change in space, or “freezes”, as it advects along a path.
This “freezing” means that the variations observed in continuous wind speed
measurements are considered a function of the advection time and are not a consequence of spatial variation along the characteristic dimension of the eddy.
The Taylor simplification is useful in cases where eddy properties evolve over a
longer time by comparison to the displacement of its entire characteristic dimension. Under these circumstances, the internal changes of the eddies are minimal
throughout the dislocation period, and all the characteristic dimensions are retained
at the measurement point. Taylor’s hypothesis can be expressed as follows:
@U
@t
¼ Àu
@U
@x
À v
@U
@y
À w
@U
@z
ð3:26Þ
where U is a scalar or vectorial variable and u, v, and w, are the wind speed
components in x, y, and z directions.
Turbulence is frozen when:
r v 0:5U
ð3:27Þ
where U is the mean wind speed and r its standard deviation (Willis and Deardoff
1976). The Taylor hypothesis can be used when the turbulence intensity is low
relative to the mean flow.
3.4 Ergodic Conditions
It is convenient to simplify the measurement of time-dependent variables using
rules and averages (Eqs. 3.1, 3.10, and 3.18) for obtaining continuous microclimatic
data, using sensors installed at a given point. Taylor’s premise for calculating the
means should, in principle, deal with time and space separately. That is, for a given
variable B (t, s) which is a function of time and space, the average time over a total
period of measurement t will be
t BðsÞ ¼
1
N
X NÀ1
i¼0
Aði; sÞ
ð3:28Þ
where the i index is the number of time increments Dt and t = iDt. The corresponding spatial mean becomes
3.3 Taylor’s Hypothesis
39
This “freezing” means that the variations observed in continuous wind speed
measurements are considered a function of the advection time and are not a consequence of spatial variation along the characteristic dimension of the eddy.
The Taylor simplification is useful in cases where eddy properties evolve over a
longer time by comparison to the displacement of its entire characteristic dimension. Under these circumstances, the internal changes of the eddies are minimal
throughout the dislocation period, and all the characteristic dimensions are retained
at the measurement point. Taylor’s hypothesis can be expressed as follows:
@U
@t
¼ Àu
@U
@x
À v
@U
@y
À w
@U
@z
ð3:26Þ
where U is a scalar or vectorial variable and u, v, and w, are the wind speed
components in x, y, and z directions.
Turbulence is frozen when:
r v 0:5U
ð3:27Þ
where U is the mean wind speed and r its standard deviation (Willis and Deardoff
1976). The Taylor hypothesis can be used when the turbulence intensity is low
relative to the mean flow.
3.4 Ergodic Conditions
It is convenient to simplify the measurement of time-dependent variables using
rules and averages (Eqs. 3.1, 3.10, and 3.18) for obtaining continuous microclimatic
data, using sensors installed at a given point. Taylor’s premise for calculating the
means should, in principle, deal with time and space separately. That is, for a given
variable B (t, s) which is a function of time and space, the average time over a total
period of measurement t will be
t BðsÞ ¼
1
N
X NÀ1
i¼0
Aði; sÞ
ð3:28Þ
where the i index is the number of time increments Dt and t = iDt. The corresponding spatial mean becomes
3.3 Taylor’s Hypothesis
39