Geoscience Reference
In-Depth Information
such a gradient can persist (rather than being
destroyed by air motion towards the low pressure)
results from the effect of the earth's rotation in
giving rise to the Coriolis force.
Path relative
to frame
1 The pressure-gradient force
The pressure-gradient force has vertical and
horizontal components but, as already noted, the
vertical component 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 air mass. 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
Path
relative
to rotating
disc
ti
at
Figure 6.1
The Coriolis deflecting force operating
on an object moving outward from the center of a
rotating turntable.
center 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 coordinates
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 center 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 centrifugal force is involved. In the case
of the rotating earth (with rotating reference
coordinates 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 mathematician G.G. Coriolis in
the 1830s. The 'force' (per unit mass) is expressed
by:
1d
p
------
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. The pressure-
gradient force is also inversely proportional to
air density, and this relationship is of particular
importance in understanding the behavior of
upper winds.
2 The earth's rotational deflective
(Coriolis) force
The Coriolis force arises from the fact that the
movement of masses over the earth's surface is
referenced to a moving coordinate system (i.e., the
latitude and 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
-2
Ω
V
sin
φ
