Geoscience Reference
In-Depth Information
Figure 11.6 An idealization of mean wind and stress profiles in the barotropic
CBL.
w
e
is the entrainment velocity,
Section 11.4.2
;
x
and
U
are in the direction
of the mean wind in the surface layer.
Starting at the surface,
U
increas
es w
ith
z
and
V
is zero. In the mixed layer
U
is
constant and
V
remains zero. As
uw
decreases linearly to zero at the ABL top its
gradient is constant at
u
2
/z
i
andsothe
U
-momentum
equation (11.6)
is
∗
u
2
u
2
z
i
=−
∗
fV
g
,
so that
V
g
=−
fz
i
.
(11.7)
Within the mixed layer
∂V/∂z
0sothat
vw
0, and from the second of
Eqs.
(11.6)
U
U
g
there.
The adjustment
V
If the wind turning angle is
α
,thentan
α
→
u
2
=
V
g
/U
g
−
/f U z
i
.
This is typically
∗
u
2
of the order of
u
∗
/U
, which is small, so tan
α
/f U z
i
. Thus, the wind
turning angle can be only a few degrees, much smaller than typical values in neutral
or stable ABLs. Finally, as discussed in
Section 11.4.1
entrainment of the inversion
at velocity
w
e
in the presence of a mean velocity jump
V
generates a lateral stress
−
w
e
V
α
−
∗
w
e
αU
w
e
u
2
/f z
i
at the inversion base, as sketched.
∗
11.2.3.2 The baroclinic case
The meanwind and stress profiles sketched in
Figure 11.6
a
re not typically observed
in the CBL because naturally occurring horizontal temperature gradients are apt to
make it baroclinic.
Equation (11.4)
says baroclinity is balanced in steady conditions
by a Coriolis term involving mean wind shear and a term involving the curvature of
the stress profile. A natural question then is whether turbulent mixing can minimize
the mean wind shear so that the baroclinity is balanced mainly by the latter.
Figure
unstable (
−
z
i
/L
=
250) baroclinic CBL over land, gives little support to this
notion.
