Geography Reference
In-Depth Information
Fig. 3.4
Force balance in cyclostrophic flow:
P designates the pressure gradient and
Ce
the centrifugal force.
a preferred direction of rotation. According to data collected by Sinclair (1965),
they are observed to be anticyclonic as often as cyclonic.
3.2.5
The Gradient Wind Approximation
Horizontal frictionless flow that is parallel to the height contours so that the tan-
gential acceleration vanishes (DV /Dt
0) is called
gradient flow
. Gradient flow
is a three-way balance among the Coriolis force, the centrifugal force, and the hor-
izontal pressure gradient force. Like geostrophic flow, pure gradient flow can exist
only under very special circumstances. It is always possible, however, to define
a gradient wind, which at any point is just the wind component parallel to the
height contours that satisfies (3.10). For this reason, (3.10) is commonly referred
to as the gradient wind equation. Because (3.10) takes into account the centrifugal
force due to the curvature of parcel trajectories, the gradient wind is often a better
approximation to the actual wind than the geostrophic wind.
The gradient wind speed is obtained by solving (3.10) for
V
to yield
=
f
2
R
2
4
1/2
fR
2
R
∂
∂n
V
=−
±
−
f
2
R
2
4
fRV
g
1/2
fR
2
=−
±
+
(3.15)
