Geoscience Reference
In-Depth Information
Figure 11.10 Left: Observed values of the time scales
τ
s
and
τ
in the model
(11.16)
of the pressure-destruction term in the stress budgets. Right: The observed
mid-CBL eddy diffusivity (ordinate) versus that predicted from the models
(11.17)
and
(11.18)
.From
Wyngaard
(
1984
).
(11.18)
at
z
0
.
5
z
i
in the Minnesota and AMTEX experiments, as functions of
the parameter
w
∗
z
i
[1
B)/S
]. This plot also includes midlayer
K
s
m
and
K
m
values estimated from Deardorff's (1974) LES results
†
for hours 14 and 15,
respectively, of day 33 of the Wangara experiment. This plot shows no significant
difference between
K
s
m
and
K
m
and suggests that
K
m
+
+
(T
0
.
05
w
∗
z
i
in mid-CBL.
The factor 1 +
(T
B)/S
varied from about 0.6 to 1.25 in mid-CBL, suggesting
the range of variation of that
K
m
value.
As we discussed in
Chapter 10
,
Subse
ctio
n 10.2.4.5
, if we write the t
ime
-change
a
nd h
orizontal advection terms in the
uw
budget, for example, as
uw/τ
u
and
Uuw/L
x
, with
τ
u
and
L
x
the scales of the unsteadiness and inhomogeneity, then if
τ
u
+
τU
the quasi-steady, locally homogeneous assumptions under-
lying
Eq. (11.17)
are valid, and likewise for
Eq. (11.18) (Problem 11.18)
.Using
τ
τ
and
L
x
1000 m,
U
=10ms
−
1
,and
w
∗
=
1ms
−
1
,
=
0
.
1
z
i
/w
∗
(Figure 11.10)
,
z
i
=
these are
τ
u
1000 m. In many situations these criteria should
not be difficult to satisfy. Then if in addition the stress budget behavior on which
Eqs. (11.17)
and
(11.18)
are based holds over a reasonable range of
100 s,
L
x
−
z
i
/L
values,
these eddy-diffusivity expressions could be useful in applications.
†
Deardorff's LES calculation, which used 40
3
grid points on a CDC 6600 “mainframe” computer, ran a factor of
10 slower than real time. In late 2007 a comparable 40
3
LES code on a dedicated, single processor of an IBM
SP5 ran 16 times faster than real time - a factor of 160 faster than Deardorff's code. (Peter Sullivan, personal
communication.)
