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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)
 
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