Geoscience Reference
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Figure 4.1 A sketch of the profiles of vertical turbulent temperature flux (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
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 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
∂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.
 
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