Geoscience Reference
In-Depth Information
Figure 13.4 The probability density of vertical velocity at three heights in a CBL
as determined from LES results.
z
i
is the boundary-layer depth and
w
is the
∗
convective velocity scale. From
Lamb
(
1982
).
are generally consistent with this.
Lamb
(
1982
) attributes these unusual properties
of dispersion in the CBL to the large Lagrangian integral time scale and the highly
skewed pdf of its vertical velocity.
13.3.3 Joint probability densities
Wyngaard and Moeng
(
1992
) determined the joint probability density (jpd) of
w
and mixing ratio
c
of a passive, conserved scalar through analysis of the fields
obtained through LES of a CBL. In general this joint density has the property
∞
∞
β(w
,c
)dw
dc
=
1
;
−
C
−∞
∞
∞
β(w
,c
)w
c
dw
dc
=
wc.
(13.31)
−
C
−∞
(The lower limit of the
c
-integral corresponds to
C
.)
The jpds for
w
with the top-down and bottom-up fields
c
t
and
c
b
are shown in
Figures 13.5
and
13.6
.
They agree quite well with those measured by
Deardorff and
so that
c
˜
=
C
+
c
=
0
,c
=−
β
∗
d
w
σ
w
d
c
β
∗
=
σ
w
σ
c
β,
σ
c
=
1
.
(13.32)
†
Wyngaard and Moeng
(
1992
) commented that the laboratory jpds seem not to integrate to 1.0 over the plane
and suggested that an error was made in their scaling. We confirmed that error and corrected it.
