Geoscience Reference
In-Depth Information
We have neglected the Coriolis and viscous dissipation terms, the first because it is
small in the ABL and the second through local isotropy,
Chapter 14
.
In the unstable surface layer the Kansas results (
Wyngaard et al.
,
1971
)showa
three-way balance among shear production (the primary source), buoyant produc-
tion (the secondary source), and the loss to the pressure-destruction term. Given the
highly variable instantaneous nature of the unstable s
urfa
ce layer, one might have
expected a significant turbulent transport term in the
uw
budget, but instead it is
small, on the order of 10% or less of the principal terms. This reminds us that local,
instantaneous structure reveals nothing abou
t ex
pected values, and vice versa.
To a good approximation the near-neutral
uw
budget is
w
2
∂U
∂z
=
rate of loss to pressure term
.
(10.46)
If we write the loss term as
uw/τ
,where
τ
is a time scale, then
Eq. (10.46)
reduces to the eddy-diffusivity form
−
w
2
τ
∂U
uw
∼−
∂z
.
(10.47)
10.4.4 The
wθ
budget
From
(8.70)
in quasi-steady conditions this is
w
2
∂
∂
∂z
wwθ
ρ
0
θ
∂p
1
g
θ
0
θ
2
.
∂z
+
=−
∂z
+
(10.48)
The Kansas results (
Wyngaard et al.
,
1971
) show that in nea
r-ne
utral conditions
the buo
yanc
y and transport terms are negligible. Thus, like the
uw
budget the near-
neutral
wθ
budget reduces to a balance between mean-gradient production and
pressure destruction:
w
2
∂
ρ
0
θ
∂p
1
∂z
=−
∂z
.
(10.49)
If we model the latter as
−
wθ/τ
,where
τ
is a time scale, then we have
w
2
τ
∂
wθ
=−
∂z
,
(10.50)
as for the stress budget.
While there is overall similarity here between
the
the
uw
and
wθ
budgets, the
buoyancy term is relatively more important for
wθ
. This gives a hint that under
unstable conditions the coupling between turbulent flux and mean gradient for