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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 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)
 
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