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3.d. Intensity of convection (3): Transition layer
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Figure 8: Vertical one-dimensional "chimney"
convective plume model.
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According to the argument in
Intensity of convection (2),
potential temperature difference
of the conduction layer in daytime
is expected to be more than 6 K.
However, the potential temperature deviation of ascending
convective plumes in convection layer is about 2 K.
This difference is caused by the entrainment of the
relatively cold air surrounding an ascending plume
during the layer of moderate vertical
gradient of temperature
between the conduction layer and the convective layer.
In the followings, the region where entrainment occurs
is referred to as the transition layer.
Let us consider influence of entrainment on the potential
temperature deviation of convective plumes.
Assume that,
at the root of a plume as illustrated by the blue frame in
Figure 8,
air with the potential temperature of
is coming up from the below of the transition layer
at the velocity of
 ,
and air with the potential temperature of
is going out to the convection layer
at the velocity of
 .
We have
by considering the heat budget.
Now, can be estimated by
the buoyancy force of convective plume ascending from the
conduction layer and the turbulent diffusion time of the
conduction layer,
 ,
while
can be estimated from the work done
by convective plume in the convection layer.
 is the depth of the convection
layer.
If we define  ,
which is the time for the convective plume to
travel around the convection layer with its potential
temperature deviation kept constant,
can be rewritten as
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(5) |
The influence of entrainment is determined by the ratio
of the travel time of plume to turbulent diffusion time.
By assuming that
is given as the potential
temperature difference of the conduction layer,
we can estimate the potential temperature deviation
of a convective plume
in the convection layer
by the use of (5).
Suppose daytime at LT = 14:00.
From Figure 7,
we can adopt
 ˜ 40 m and ˜ 6 K.
By using these values,
which roughly coincides with those of plumes observed at LT=14:00.
According to the above discussion, potential
temperature deviation of ascending convective plumes can
be estimated by using heat flux  ,
depth of convection layer ,
and turbulent diffusion coefficient  .
Note that this estimation does not describe causality of
the whole convection field, since
the magnitude of sensible heat flux included in
and the value of turbulent diffusion coefficient are
determined by the convective motion to be determined
itself.
Note also that the estimation by the use of (5) can be applied only for the case
where convection is well developed and hence
 <
can be assumed.
When
>
,
we have a strange result,
>
,
which means that
potential temperature deviation of convective plumes is
larger than potential temperature difference in the
conduction layer.
In such a case, it is more reasonable to assume that
entrainment hardly occurs.
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