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Figure 10.8 The TKE budget in the unstable surface layer.
B
is buoyant production;
P
is pressure transport;
S
is shear production;
T
is turbulent transport;
is viscous
dissipation. Terms are nondimensionalized with
kz
,
u
, and
Q
0
.
From
Wyngaard
(
1992
). Reprinted, with permission, from
Annual Review of Fluid Mechanics
,
24
,
© 1992 by Annual Reviews, www.annualreviews.org.
∗
a balance among mean-gradient production, turbulent transport, and molecular
destruction. For the entire stability range, the Kansas data indicate that mean-
gradient production is the principal source term and that turbulent transport is at
least an order of magnitude smaller. Therefore, in the unstable surface layer this bud-
get is to first approximation in
local balance
- mean-gradient production balances
molecular destruction. Measurements by
Bradley
et al.
(
1981b
) confirm this.
The budget of water vapor mixing ratio (
q
)
vari
ance
has
the same form, but the
difference in the buoyant production terms for
qw
and
θw
(Section 10.2.3)
has an
impact on the variances
(Problem 10.20)
. In the surface layer the scaled variance of
q
is a factor of 2-3 larger, and the scaled molecular destruction rate is about 30%
larger (
Katul and Hseih
,
1999
).
10.4.3 The shear-stress budget
The quasi-steady budget of the principal component of kinematic shear stress
uw
is, from
Eq. (8.70)
,
w
∂p
w
2
∂U
∂
∂z
uww
1
ρ
0
u
∂p
∂z
g
θ
0
θu.
∂z
+
=−
∂x
+
+
(10.45)