Geoscience Reference
In-Depth Information
1 The pressure-gradient force
longitude grid, which 'rotates' with the earth). The
simplest way to visualize how this deflecting force
operates is to picture a rotating disc on which moving
objects are deflected. Figure 6.1 shows the effect of such
a deflective force operating on a mass moving outward
from the centre of a spinning disc. The body follows
a straight path in relation to a fixed frame of reference
(for instance, a box that contains the spinning disc), but
viewed relative to co-ordinates rotating with the disc the
body swings to the right of its initial line of motion.
This effect is readily demonstrated if a pencil line is
drawn across a white disc on a rotating turntable. Figure
6.2 illustrates a case where the movement is not from
the centre of the turntable and the object possesses an
initial momentum in relation to its distance from the
axis of rotation. Note that the turntable model is not
strictly analogous since the outwardly directed cen-
trifugal force is involved. In the case of the rotating
earth (with rotating reference co-ordinates of latitude
and longitude), there is apparent deflection of moving
objects to the right of their line of motion in the northern
hemisphere and to the left in the southern hemisphere,
as viewed by observers on the earth. The idea of a
deflective force is credited to the work of French math-
ematician G.G. Coriolis in the 1830s. The 'force' (per
unit mass) is expressed by:
The pressure-gradient force has vertical and horizontal
components but, as already noted, the vertical com-
ponent is more or less in balance with the force of
gravity. Horizontal differences in pressure arise from
thermal heating contrasts or mechanical causes such
as mountain barriers and these differences control the
horizontal movement of an airmass. The horizontal
pressure gradient serves as the motivating force that
causes air to move from areas of high pressure towards
areas where it is lower, although other forces prevent
air from moving directly across the isobars (lines of
equal pressure). The pressure-gradient force per unit
mass is expressed mathematically as
1d
p
- — —
ρ
d
n
where
= air density and d
p
/d
n
= the horizontal gradient
of pressure. Hence the closer the isobar spacing the more
intense is the pressure gradient and the greater the wind
speed (Figure 6.1). The pressure-gradient force is also
inversely proportional to air density, and this relation-
ship is of particular importance in understanding the
behaviour of upper winds.
ρ
-2 Ω
V
sin φ
2 The earth's rotational deflective
(Coriolis) force
where Ω = the angular velocity of spin (15°hr
-1
or 2π/24
rad hr
-1
for the earth = 7.29
10
-5
rad s
-1
);
φ
= the
The Coriolis force arises from the fact that the move-
ment of masses over the earth's surface is referenced
to a moving co-ordinate system (i.e. the latitude and
latitude and
V
= the velocity of the mass. 2
Ω
sin
φ
is
referred to as the Coriolis parameter (
f
).
The magnitude of the deflection is directly pro-
portional to: (1) the horizontal velocity of the air (i.e.
air moving at 10 m s
-1
has half the deflective force
operating on it as on that moving at 20 m s
-1
); and (2)
the sine of the latitude (sin 0 = 0; sin 90 = 1). The effect
is thus a maximum at the poles (i.e. where the plane of
the deflecting force is parallel to the earth's surface).
It decreases with the sine of the latitude, becoming zero
at the equator (i.e. where there is no component of the
deflection in a plane parallel to the surface). The Coriolis
'force' depends on the motion itself. Hence, it affects
the direction but not the speed of the air motion, which
would involve doing work (i.e. changing the kinetic
energy). The Coriolis force always acts at right-angles
to the direction of the air motion, to the right in the
northern hemisphere (
f
positive) and to the left in
Path relative
to frame
Path
relative
to rotating disc
c
t
Figure 6.1
The Coriolis deflecting force operating on an object
moving outward from the centre of a rotating turntable.
