These authors indicate turbulent intensity values from 0.2 to 0.45 for hardwood
stands within the limits (i u < 0.5) using Taylor's hypothesis (turbulent freezing) for
measurements at a single point. The turbulent intensities are ordered as follows:
i w \ i v \ i u
ð4:9Þ
The turbulent kinetic energy budget in the forest roughness sublayer requires
terms in relation to the formation of turbulent wakes downwind from the surface
elements. This turbulence associated with the development of wakes can be significant, about twice the magnitude of turbulence from tangential interaction with
the mean velocity field (Raupach and Shaw 1982).
Coppin et al. (1986) consider that wake turbulence production, P w , within
canopies, can be quantified as
P w ¼ u
@ u 0 w 0
À
Á
@z
*
+
ð4:10Þ
wherein angle brackets represent the horizontal average operator. This equation is
obtained from spatial averaging of the turbulent kinetic energy (Eqs. 3.88 and 3.89)
and accounts to produce turbulent kinetic energy (TKE) from the mean kinetic
energy (MKE). The energy converted by wake production from MKE to TKE is
equally done on the work done on the mean flow by canopy elements producing
form drag (Raupach and Thom 1981).
Leclerc et al. (1990), based on results from the hardwood canopy atmospheric
surface layer at Camp Borden, Canada, suggest that conditions of thermal stability
are more conducive to kinetic energy development resulting from wake turbulence
(Eq. 4.10). The wake turbulence corresponds to eddies with a maximum length
scale that must be smaller than those relative to momentum transport. Thus, the
absorption of momentum by aerodynamic drag on the foliage is linked to an
accelerated rate of viscous dissipation of turbulent kinetic energy (Baldocchi and
Mayers 1988). The wake effect induced by forest canopies draws kinetic energy
from average mean flow and to large intermittent descending eddies (Raupach and
Thom 1981).
Data from Leclerc et al. (1990) are presented in Fig. 4.4 that show the effect of
conditions of instability and thermal neutrality in the terms for the kinetic energy
budget equation (Eq. 3.89):
@e
@t
¼
g
h v
u 0
3 h
0
v
À
@ u 0
3 e
À Á
@x 3
À
1
q
@ u 0
3 p 0
À
Á
@x 3
À u 0
1 u 0
3
@u 1
@x 3
À
I
III
IV
V
VI
VII
ð3:89Þ
114
4 Exchange of Energy and Mass Over Forest Canopies
stands within the limits (i u < 0.5) using Taylor's hypothesis (turbulent freezing) for
measurements at a single point. The turbulent intensities are ordered as follows:
i w \ i v \ i u
ð4:9Þ
The turbulent kinetic energy budget in the forest roughness sublayer requires
terms in relation to the formation of turbulent wakes downwind from the surface
elements. This turbulence associated with the development of wakes can be significant, about twice the magnitude of turbulence from tangential interaction with
the mean velocity field (Raupach and Shaw 1982).
Coppin et al. (1986) consider that wake turbulence production, P w , within
canopies, can be quantified as
P w ¼ u
@ u 0 w 0
À
Á
@z
*
+
ð4:10Þ
wherein angle brackets represent the horizontal average operator. This equation is
obtained from spatial averaging of the turbulent kinetic energy (Eqs. 3.88 and 3.89)
and accounts to produce turbulent kinetic energy (TKE) from the mean kinetic
energy (MKE). The energy converted by wake production from MKE to TKE is
equally done on the work done on the mean flow by canopy elements producing
form drag (Raupach and Thom 1981).
Leclerc et al. (1990), based on results from the hardwood canopy atmospheric
surface layer at Camp Borden, Canada, suggest that conditions of thermal stability
are more conducive to kinetic energy development resulting from wake turbulence
(Eq. 4.10). The wake turbulence corresponds to eddies with a maximum length
scale that must be smaller than those relative to momentum transport. Thus, the
absorption of momentum by aerodynamic drag on the foliage is linked to an
accelerated rate of viscous dissipation of turbulent kinetic energy (Baldocchi and
Mayers 1988). The wake effect induced by forest canopies draws kinetic energy
from average mean flow and to large intermittent descending eddies (Raupach and
Thom 1981).
Data from Leclerc et al. (1990) are presented in Fig. 4.4 that show the effect of
conditions of instability and thermal neutrality in the terms for the kinetic energy
budget equation (Eq. 3.89):
@e
@t
¼
g
h v
u 0
3 h
0
v
À
@ u 0
3 e
À Á
@x 3
À
1
q
@ u 0
3 p 0
À
Á
@x 3
À u 0
1 u 0
3
@u 1
@x 3
À
I
III
IV
V
VI
VII
ð3:89Þ
114
4 Exchange of Energy and Mass Over Forest Canopies