Geoscience Reference
In-Depth Information
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
exactly balanced 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 (
Vg
) of which is
given by the following formula:
1 d
p
Vg
= --------- ---
2
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 continually change 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 unfortunate
oversimplification of reality.
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 speed of 15m s
-1
at latitude 43
4 The centripetal acceleration
For a body to follow a curved path there must be
an inward acceleration (
c
) towards the center of
rotation. This is expressed by:
mV
2
c
= - ----
r
°
will produce a velocity of only 10m s
-1
at latitude
90°. Except in low latitudes, where the Coriolis
parameter approaches zero, the geostrophic wind
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 radially 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 center. It is
therefore only necessary to consider the forces
involved in the rotation of the air around a local
axis of high or low pressure. Here the curved path
of the air (parallel to the isobars) is maintained by
an inward-acting, or centripetal, acceleration.
Figure 6.4
shows (for the Northern Hemi-
sphere) that in a low pressure system balanced
flow is maintained in a curved path (referred to as
the
gradient wind
) by the Coriolis force being
weaker than the pressure force. The difference
between the two gives the net centripetal accelera-
tion inward. In the high pressure case, the inward
acceleration exists because the Coriolis force
(A)
Low
P
Pressure
force
500gpm
GEOSTROPHIC
WIND, V
g
540gpm
Coriolis
force
C
High
(B)
V
Low
V-Vg
V-V
g
1000mb
V
g
1004mb
High
F
C
Resultant of the Coriolis
and friction force
Figure 6.3
A: The geostrophic wind case of
balanced motion (Northern Hemisphere) above the
friction layer (contour heights are gpm) B: Surface
wind
V
represents a balance between the geo-
strophic wind,
V
g,
and the resultant of the Coriolis
force (
C
) and the friction force (
F
). Note that
F
is not
generally directly opposite to the surface wind.
