Page 302 - Fundamentals of Air Pollution

258 17. The Physics of the Atmosphere

A. Pressure Gradient Force
Three forces of importance to horizontal motion are the pressure gradient
force, gravity, and friction. Atmospheric pressure equals mass times the
acceleration of gravity. Considering a unit volume, p = pg; the gravitational
force on the unit volume is directed downward. Primarily because of hori-
zontal temperature gradients, there are horizontal density gradients and
consequently horizontal pressure gradients. The horizontal pressure gradi-
ent force p h = Ap/p Ax where Ap is the horizontal pressure difference over
the distance AJ. The direction of this force and of the pressure difference
measurement is locally perpendicular to the lines of equal pressure (isobars)
and is directed from high to low pressure.

B. Coriolis Force

If the earth were not rotating, the wind would blow from high to low
pressure. Close to the earth, it would be slowed by friction between the
atmosphere and the earth's surface but would maintain the same direction
with height. However, since the earth undergoes rotation, there is an
apparent force acting on horizontal atmospheric motions when examined
from a point of reference on the earth's surface. For example, consider a
1
wind of velocity 10 m s" blowing at time 1 in the direction of the 0°
longitude meridian across the north pole (Fig. 17-10). The wind in an
absolute sense continues to blow in this direction for 1 hr, and a parcel of
air starting at the pole at time 1 travels 36 km in this period. However,
since the earth turns 360° every 24 hr, or 15° per hr, it has rotated 15° in
the hour and we find that at time 2 (60 min after time 1) the 15° meridian
is now beneath the wind vector. As viewed from space (the absolute frame
of reference), the flow has continued in a straight line. However, as viewed
from the earth, the flow has undergone an apparent deflection to the right.
The force required to produce this apparent deflection is the coriolis force
and is equal to D = vf where /, the coriolis parameter, equals 2ft sin <£.

Fig. 17-10. Effect of the coriolis force. The path of air moving from the north pole to the
south as viewed from space is straight; as viewed from the earth's surface it is curved.