Geoscience Reference
In-Depth Information
Figure 4.1 A sketch of the profiles of vertical turbulent temperature flux
wθ
(left)
and mean temperature
(right) in a growing convective boundary layer. In mid
day
∂/∂z
can vanish in midlayer; those points are indicated by dashed lines. If
wθ
is nonzero at those points (as at the later times, left) the eddy diffusivity
K
has a
singularity there; for some distance above that
K
is negative. Here “temperature”
is potential temperature (
Part II
).
behaved; it has a singularity if
∂/∂z
and
wθ
change sign at different heights, as
at the later times in
Figure 4.1
.
The complete mean-temperature
equation (4.2)
for the one-dimensional problem
reduces to
wθ
∂
∂t
+
∂
∂z
α
∂
∂z
−
=
0
.
(4.4)
A typical value of the surface temperature flux
Q
0
over land on a sunny day is
0.1m s
−
1
K, which requires a mean temperature gradient at the surface of
∂
∂z
=−
Q
0
10
4
Km
−
1
,
α
∼−
(4.5)
10
−
5
m
2
s
−
1
.
Above the thin diffusive sublayer the temperature flux is carried almost entirely
by the turbulence. The eddy diffusivity is of order
u
, much larger than
α
,sothe
magnitude of
∂/∂z
is much less than at the surface. At a height
z
using
α
=
h
where
10
5
α
, for example, which we shall see in
Part II
occurs
in the surface layer, turbulence reduces
∂/∂z
to
∼
the eddy diffusivity is
0
.
1Km
−
1
, five orders of
∼
magnitude smaller than at the surface.