Geoscience Reference
In-Depth Information
fraction of the flow volume as
R
t
increases, and so they become more intense with
increasing
R
t
. This is reflected in the broadening of the tails of the pdf of a velocity
derivative as
R
t
increases, which causes the skewness and kurtosis of the velocity
derivative to increase with
R
t
(Chapter 7)
.
Direct numerical simulation (DNS) of turbulence is currently limited by computer
size to about 10
10
grid points, a few thousand in each of the three spatial directions.
Roughly, then, the maximum attainable values of
/η
are currently
10
3
, whereas
in the atmospheric boundary layer
/η
can be as large as 10
6
.Since
/η
is a
surrogate for the turbulence Reynolds number,
Eq. (1.35)
, fine structure computed
from DNS is not a reliable indicator - not even qualitatively - of the fine structure
of atmospheric turbulence.
∼
13.3.2.2 Vertical velocity in the CBL
In 1975 some intriguing evidence of unusual behavior of neutrally buoyant effluent
plumes in the CBL came from experiments done in a laboratory convection tank.
As described by
Willis and Deardorff
(
1974
), the 114 cm
76 cm
deep tank, using water heated from below, generated turbulent free convection of
modest Reynolds number
(R
t
×
122 cm
×
4200
,R
λ
140
)
. In their experiments
Deardorff
andWillis
(
1975
) used a near-surface, crosswind line source of effluent. The unusual
behavior was the ascent of the mean plume as it moved downstream; by a travel time
of the order of
h/w
∗
it reached a height of about 0
.
75
h
, with
h
the CBL depth. As
discussed by
Lamb
(
1982
), this finding stimulated great interest but also skepticism
that a convection tank could model diffusion in the CBL.
Lamb
(
1978
) described a similar phenomenon in a numerical model calculation
of plume dispersion from an elevated source in the CBL: the locus of maximum
mean concentration downstream of an elevated source descends until it reaches the
surface. Motivated by these numerical results,
Willis and Deardorff
(
1978
) carried
out elevated-source experiments in their convection tank and found plume-descent
there.
Lamb
(
1982
) describes the two sets of results as being in “remarkably good
agreement.”
†
These findings on effluent-plume dispersion in the CBL stimulated interest in the
probability density of vertical velocity fluctuations.
Figure 13.4
,
from
Lamb
(
1982
),
shows that probability density for
w
computed by Deardorff through LES in a
5km
2 km deep domain. It is strongly positively skewed (
w
3
>
0
)
.The
mode, or most probable velocity, is negative; it is approximately equal to the mean
downdraft velocity. About 60% of the area under the density is on the negative half
of the
w
-axis, indicating the higher probability of downdrafts. Field observations
×
5km
×
†
Lamb
(
1982
) also pointed out that “this is an example in which the predictions of a theoretical model were later
confirmed by observations.”
