Geography Reference
In-Depth Information
where in the lower expression (3.11) is used to express ∂/∂n in terms of the
geostrophic wind.
Not all the mathematically possible roots of (3.15) correspond to physically
possible solutions, as it is required that V be real and nonnegative. In Table 3.1
the various roots of (3.15) are classified according to the signs of
R
and ∂/∂n in
order to isolate the physically meaningful solutions
The force balances for the four permitted solutions are illustrated in Fig. 3.5.
Equation (3.15) shows that in cases of both regular and anomalous highs the
pressure gradient is limited by the requirement that the quantity under the radical
be nonnegative; that is,
fV
g
=
f
2
4
∂
∂n
<
|
R
|
(3.16)
0. It is for
this reason that the pressure field near the center of a high is always flat and the
wind gentle compared to the region near the center of a low.
The absolute angular momentum about the axis of rotation for the circularly
symmetric motions shown in Fig. 3.5 is given by VR
Thus, the pressure gradient in a high must approach zero as
|
R
|→
fR
2
/2. From (3.15) it is
verified readily that regular gradient wind balances have positive absolute angular
momentum in the Northern Hemisphere, whereas anomalous cases have negative
absolute angular momentum. Because the only source of negative absolute angular
momentum is the Southern Hemisphere, the anomalous cases are unlikely to occur
except perhaps close to the equator.
In all cases except the anomalous low (Fig. 3.5c) the horizontal components
of the Coriolis and pressure gradient forces are oppositely directed. Such flow is
+
Table 3.1
Classification of Roots of the Gradient Wind Equation in the Northern Hemisphere
Sign ∂/∂n
R>0
R<0
Positive root:
a
Positive
unphysical
Positive root: antibaric flow
(V
g
< 0)
(anomalous low)
Negative root: unphysical
Negative root: unphysical
Negative
Positive root: cyclonic flow
Positive root: (V>
−
fR/2):
(V
g
> 0)
(regular low)
anticyclonic flow (anomalous
high)
Negative root: unphysical
Negative root: (V<
fR/2):
anticyclonic flow (regular
high)
−
a
The terms “positive root” and “negative root” in columns 2 and 3 refer to the sign taken in the final
term in Eq. (3.15).
