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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 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 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
=−
∂z ,
(10.50)
as for the stress budget.
While there is overall similarity here between the the uw and budgets, the
buoyancy term is relatively more important for . This gives a hint that under
unstable conditions the coupling between turbulent flux and mean gradient for
 
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