Geoscience Reference
In-Depth Information
Figure 12.4 A schematic of the upward diffusion of stable stratification in the
young nocturnal SBL. The curve labeled
z
cw
(t)
is the mean upper edge of the dif-
fusing cooling wave; the solid portion of the curve labeled
z
s
(t)
is the mean height
above which the effects of this cooling are dynamically significant. The shaded
region between the curves is the region influenced by the stable stratification.
and
12.3
show time histories of near-surface temperature, friction velocity
u
∗
,and
Q
0
near transition in the Minnesota experiment.
Observational data on the late-afternoon CBL decay process are scarce, but LES
studies by
Nieuwstadt and Brost
(
1986
) gave some insight. They focused on a
somewhat different problem, the response of a quasi-steady CBL to the abrupt
zeroing of its surface heat flux. The decay of TKE began about one
z
i
/w
∗
time
after transition, the time scale of the decay being of order
/u
z
i
/w
∗
. The decay
of temperature variance began sooner - perhaps because in a CBL with a negligible
or even slightly positive mean potential temperature gradient it has only one source,
turbulent transport from below.
A plausible model of the mean evolution of stable stratification in the nocturnal
SBL is the following. After transition
z
cw
(t)
, the mean height of the top of the
surface-based cooling layer,
Figure 12.4
,
moves upward through turbulent diffusion.
We'll take the initial surface-layer stratification as near-neutral, the initial vertical
velocity
v
cw
of this mean cooling wave as
∼
∼
u
∗
, and the initial time trajectory of
z
cw
as
z
cw
=
v
cw
t
∼
u
∗
t.
(12.7)
At some height
z
s
<z
cw
the rate of buoyant destruction of ambient TKE caused
by the upward-diffusing stable stratification becomes dynamically important. We'll
define
z
s
as the height where the rate of buoyant destruction of TKE is a given
fraction
a<
1 of the rate of shear production:
θ
0
wθ(z
s
)
=
a uw(z
s
)
∂U
g
∂z
(z
s
).
(12.8)
