Geoscience Reference
In-Depth Information
homogeneous and driven by a pressure gradient; it had a no-slip boundary condition
on the lower wall and a free-slip (stress free) wall at the top. He computed neutral
turbulent flow as an initial condition and then continued the computations with a
constant, negative heat flux imposed at the bottom wall. He found that the flow
continued to be turbulent only for
h/L <
0
.
5
.
†
Nieuwstadt also found that weak stable stratification increased the rate of viscous
dissipation, which in equilibrium required an increase in the rate of shear pro-
duction. The interpretation is that the stable stratification, whose damping effects
are strongest for the largest eddies,
Eq. (10.38)
, decreases
and hence increases
u
3
/
. The resulting increase in the rate of shear production was larger than the
rate of loss to buoyant destruction.
∼
12.1.2 Second-order-closure modeling of the SBL
Numerical modeling has been applied to the ABL since the 1960s, and “second-
order closure” came into use in the 1970s. As in the engineering community
(Chapter 5)
, as experience was gained with the models the hopes for their uni-
versality dimmed. Fine-mesh LES “data bases” facilitated the testing of models
in atmospheric applications, and in this way
Moeng and Wyngaard
(
1989
) con-
cluded that typical shear-flow closures for dissipation rate and turbulent transport
performed poorly in the CBL.
Second-order models seemed to perform better in the SBL, where the turbulent
transport terms in second-moment budgets
(Chapter 5)
are much less important
than in the CBL and simple closures for pressure covariances appeared to suffice.
Delage
(
1974
) used an eddy-diffusivity model with a rate equation for TKE to
explore SBL structure with results that seemed quite physical. Many such studies
followed, including the second-order closure calculation of
Wyngaard
(
1975
)that
was “tuned” in part with the Kansas observations. It reproduced well the evolving
surface-layer properties measured in the 1973 Minnesota evening runs.
This model system spawned themuch simpler SBLmodel of
Brost andWyngaard
(
1978
). By neglecting the turbulent-transport, time-change, and Coriolis terms in
the second-moment equations and replacing a highly parameterized
rate equation
with
u
3
/
and a model for
, they converted the set of eleven partial differential
equations to eight algebraic equations for second moments (
Fitzjarrald
,
1979
). The
solutions of the BW set were quite similar to those of the original model system.
Nieuwstadt
(
1984
) then showed that the BW set of algebraic equation
s, w
hen
nond
imensionalized with the local kinematic str
ess
magnitude
τ(z)
(uw)
2
=[
+
(vw)
2
1
/
2
and the local vertical temperature flux
wθ(z)
, has solutions that depend
only on the local Monin-Obukhov length
]
†
1.25 in Nieuwstadt's convention, in which
L
is defined without the von Karman constant.
