Geoscience Reference
In-Depth Information
Moeng
(
1991
) also derived an expression for
K
in the flux-gradient form
(11.33)
:
−
z/z
i
+
R
c
z/z
i
) K
b
K
t
(
1
K
=
,
c
=
cw
1
/cw
0
.
(11.34)
z/z
i
) K
t
+
R
c
(z/z
i
) K
b
(
1
−
Here
K
t
and
K
b
are the top-down and bottom-up eddy diffusivities
K
t
and
K
b
modified to be compatible with the modified flux-gradient expression
(11.33)
:
z
z
i
4
/
3
1
2
7
z
z
i
2
1
3
K
b
K
t
z
z
i
z
z
i
w
∗
z
i
=
−
,
w
∗
z
i
=
−
.
(11.35)
Fiedler
(
1984
) discussed the generalization of the eddy diffusivity to the integral
form
D(z, z
)
∂
∂z
C(z
,t)dz
,
wc(z, t)
=
(11.36)
which is the physical-space version of the “spectral diffusivity”model of
Berkowicz
and Prahm
(
1979
). Stull's (
1984
) “transilient turbulence” closure is also of this
general form. Hamba's (
1993
) two-term eddy diffusivity expression for conserved
scalars,
K
2
∂
2
C
K
∂C
wc
=−
∂z
+
∂z
2
,
(11.37)
can reproduce the
Moeng andWyngaard
(
1984
) results for top-down and bottom-up
diffusion.
11.3.3 Generalized mixed-layer similarity
Equations (11.21)
and
(11.22)
generalize the mixed-layer similarity statement for
a mean scalar gradient in the quasi-steady, horizontally homogeneous mixed layer
to include the flux of the scalar at the CBL top:
∂C
∂z
=−
cw
1
cw
0
w
∗
z
i
g
t
(z/z
i
)
−
w
∗
z
i
g
b
(z/z
i
).
(11.38)
A typical profile of vertical flux of virtual potential temperature in the CBL is
sketched in
Figure 11.1
.
When
Eq. (11.38)
is used for
the negative flux of virtual
temperature at the top, caused by entrainment of the capping inversion, makes the
two terms on its rhs of opposite signs. The resulting
profile can be nearly uniform
in the CBL. This is no doubt the origin of the term
mixed layer
and the erroneous
notion that within it conserved scalars are “well mixed” (constant).
