Geoscience Reference
In-Depth Information
Figure 11.13 LES calculations of the budgets
(11.26)
of the bottom-up flux (left)
and
(11.25)
of the top-down flux (right) of a conserved scalar. The terms are
nondimensionalized with
w
1 and
1 on the abscissa is linear.
M
, mean-gradient production;
T
, turbulent transport;
B
, buoyant production;
P
, pressure destruction;
S
, subgrid term. From
Moeng and
Wyngaard
(
1986a
).
,z
i
, and the boundary flux. The scale between
−
∗
forested site. Previous attempts had been unsuccessful, in their view largely because
of the difficulty of making these measurements.
†
The
Wang
et al
.
(
2007
) results
were qualitatively consistent with those from LES but not all differences between
them could be explained.
The turbulent-flux budget (8.71) can give insight into the behavior of eddy dif-
fusivity. In horizontally homogeneous conditions it becomes, for the top-down and
bottom-up scalar cases,
c
t
∂p
∂z
,
∂c
t
w
∂t
w
2
∂C
t
∂c
t
w
2
∂z
g
θ
0
c
t
θ
1
ρ
0
=
0
=−
∂z
−
+
−
(11.25)
0
=
M
+
T
+
B
+
P
c
b
∂p
∂z
.
∂c
b
w
2
∂z
∂c
b
w
∂t
w
2
∂C
b
g
θ
0
c
b
θ
1
ρ
0
=
0
=−
∂z
−
+
−
(11.26)
The terms on the right side are
M
, mean-gradient production;
T
, turbulent transport;
B
, buoyant production; and
P
, pressure destruction.
Wyngaard
(
1986a
). They are not only asymmetric, but also quite different. The
top-down budget is dominated by the gain through mean-gradient production;
†
As discussed in
Chapter 2
, the variance of the difference between a time-averaged point measurement and the
ensemble mean scales with the integral scale/averaging length, whereas the corresponding quantity for area-
averaged LES fields scales with the square of that ratio. As a result, time-averaged single-point measurements
tend to have much more scatter than area-averaged LES results.
