Geoscience Reference
In-Depth Information
Figure 6.2
The Coriolis deflecting
force on a rotating turntable. (A) An
observer at X sees the object P and
attempts to throw a ball towards it.
Both locations are rotating anticlock-
wise. (B) The observer's position is
now X´ and the object is at P´. To the
observer, the ball appears to follow
a curved path and lands at Q. The
observer overlooked the fact that pos-
ition P was moving counterclockwise
and that the path of the ball would be
affected by the initial impulse due to
the rotation of point X.
e
t
P
′
X
Man sees object P
X
P
P
Observed
path of
ball
X
Q
A
B
the southern hemisphere (
f
negative). Absolute values
of
f
vary with latitude as follows:
speed of 15 m s
-1
at latitude 43° will produce a velocity
of only 10 m s
-1
at latitude 90°. Except in low latitudes,
where the Coriolis parameter approaches zero, the geo-
strophic wind is a close approximation to the observed
air motion in the free atmosphere. Since pressure
systems are rarely stationary, this fact implies that air
motion must change continually towards a new balance.
In other words, mutual adjustments of the wind and
pressure fields are constantly taking place. The common
'cause-and-effect' argument that a pressure gradient is
formed and air begins to move towards low pressure
before coming into geostrophic balance is an unfor-
tunate oversimplification of reality.
Latitude
0° 10°
20°
43°
90°
f
(10
-4
s
-1
)
0
0.25
0.50 1.00 1.458
The earth's rotation also produces a vertical com-
ponent of rotation about a horizontal axis. This is a
maximum at the equator (zero at the poles) and it causes
a vertical deflection upward (downward) for horizontal
west/east winds. However, this effect is of secondary
importance due to the existence of hydrostatic equi-
librium.
3 The geostrophic wind
4 The centripetal acceleration
Observations in the
free atmosphere
(above the level
affected by surface friction up to about 500 to 1000 m)
show that the wind blows more or less at right angles to
the pressure gradient (i.e. parallel to the isobars) with,
for the northern hemisphere, high pressure on the right
and low pressure on the left when viewed downwind.
This implies that for steady motion the pressure-gradient
force is balanced exactly by the Coriolis deflection
acting in the diametrically opposite direction (Figure
6.3A). The wind in this idealized case is called a
geostrophic wind
, the velocity (
V
g
) of which is given by
the following formula:
For a body to follow a curved path there must be an
inward acceleration (
c
) towards the centre of rotation.
This is expressed by:
mV
2
c
= - ——
r
where
m
= the moving mass,
V
= its velocity and
r
= the
radius of curvature. This effect is sometimes regarded
for convenience as a centrifugal 'force' operating radi-
ally outward (see Note 1). In the case of the earth itself,
this is valid. The centrifugal effect due to rotation has
in fact resulted in a slight bulging of the earth's mass in
low latitudes and a flattening near the poles. The small
decrease in apparent gravity towards the equator (see
Note 2) reflects the effect of the centrifugal force
working against the gravitational attraction directed
towards the earth's centre. It is therefore necessary only
to consider the forces involved in the rotation of the air
1
d
p
V
g
= ————
.
—
2
Ω
sin
φ
d
n
where d
p
/d
n
= the pressure gradient. The velocity is
inversely dependent on latitude, such that the same
pressure gradient associated with a geostrophic wind
