Geoscience Reference
In-Depth Information
Figure 11.2 Left: Vertical and horizontal velocity variances in the CBL. Dashed
lines, convection tank; solid line, asymptotic behavior of Kansas surface-layer
data; open circles, Minnesota data; solid symbols, Ashchurch, England, data. From
Caughey
(
1982
). Right: Mixed-layer scaling fails for water-vapor fluctuations
when their principal source is the entrainment process at CBL top. The dashed line
is the observed behavior of a conserved scalar in the very unstable surface layer,
Figure 10.4
.
From
Wyngaard
(
1988
).
11.2.2 The TKE budget
Equation (8.69)
yields the TKE budget in the horizontally homogeneous ABL
(Problem 11.20)
:
uw
∂U
1
2
∂u
i
u
i
∂t
vw
∂V
∂z
∂
∂z
u
i
u
i
w
2
1
ρ
0
∂
∂z
pw
g
θ
0
θw
=−
∂z
+
−
−
+
−
.
(11.2)
The terms on the right side are, in order, shear production (
S
); turbulent transport
(
T
); pressure transport (
P
); buoyant production (
B
); and viscous dissipation.
Figure 11.3
shows its behavior within the quasi-steadymixed layer as determined
from tower, balloon, and aircraft observations. The terms have been made dimen-
sionless with the mixed-layer-similarity group
w
3
/z
i
=
gQ
0
/θ
0
,whichmakes
the dimensionless buoyant production term 1.0 at the surface. Pressure transport
(which was not measured directly, but taken as the imbalance of the other terms)
is a gain term in the unstable surface layer, as also shown in
Figure 10.8
.
The
turbulent-transport term also behaves as in the unstable surface layer.
∗
11.2.3 The mean momentum balance
The steady, horizontally homogeneous mean horizontal momentum balance is
∂uw
∂z
=−
1
ρ
0
∂P
∂x
+
∂vw
∂z
=−
1
ρ
0
∂P
∂y
−
fV,
fU.
(11.3)