Geography Reference
In-Depth Information
Table 1.4
Scales of Atmospheric Motions
Type of motion
Horizontal scale (m)
10
−
7
Molecular mean free path
10
−
2
-10
−
1
Minute turbulent eddies
10
−
1
-1
Small eddies
Dust devils
1 - 10
10 - 10
2
Gusts
10
2
Tornadoes
10
3
Cumulonimbus clouds
10
4
-10
5
Fronts, squall lines
10
5
Hurricanes
10
6
Synoptic cyclones
10
7
Planetary waves
governing equations. However, before deriving the complete momentum equation
it is useful to discuss the nature of the forces that influence atmospheric motions.
These forces can be classified as either
body forces
or
surface forces
. Body forces
act on the center of mass of a fluid parcel; they have magnitudes proportional to the
mass of the parcel. Gravity is an example of a body force. Surface forces act across
the boundary surface separating a fluid parcel from its surroundings; their magni-
tudes are independent of the mass of the parcel. The pressure force is an example.
Newton's second law of motion states that the rate of change of momentum (i.e.,
the acceleration) of an object, as measured relative to coordinates fixed in space,
equals the sum of all the forces acting. For atmospheric motions of meteorological
interest, the forces that are of primary concern are the pressure gradient force, the
gravitational force, and friction. These
fundamental
forces are the subject of the
present section. If, as is the usual case, the motion is referred to a coordinate system
rotating with the earth, Newton's second law may still be applied provided that
certain
apparent
forces, the centrifugal force and the Coriolis force, are included
among the forces acting. The nature of these apparent forces is discussed in
Section 1.5.
1.4.1
Pressure Gradient Force
We consider an infinitesimal volume element of air, δV
δxδyδz, centered at
the point x
0
, y
0
, z
0
as illustrated in Fig. 1.1. Due to random molecular motions,
momentum is continually imparted to the walls of the volume element by the
surrounding air. This momentum transfer per unit time per unit area is just the
pressure exerted on the walls of the volume element by the surrounding air. If the
pressure at the center of the volume element is designated by p
0
, then the pressure
on the wall labeled A in Fig. 1.1 can be expressed in a Taylor series expansion as
=
∂p
∂x
δx
2
+
p
0
+
higher order terms
