Geography Reference
In-Depth Information
In dynamic meteorology it is customary to use the height above mean sea level
as a vertical coordinate. If the mean radius of the earth is designated by
a
and
the distance above mean sea level is designated by z, then neglecting the small
departure of the shape of the earth from sphericity, r
=
a
+
z. Therefore, (1.3) can
be rewritten as
g
0
g
∗
=
(1.4)
z/a)
2
(1
+
where
g
0
(GM/a
2
)(
r
/r) is the gravitational force at mean sea level. For
meteorological applications, z
=−
a so that with negligible error we can let
g
∗
=
g
0
and simply treat the gravitational force as a constant.
1.4.3
Viscous Force
Any real fluid is subject to internal friction (viscosity), which causes it to resist
the tendency to flow. Although a complete discussion of the resulting
viscous
force
would be rather complicated, the basic physical concept can be illustrated
by a simple experiment. A layer of incompressible fluid is confined between two
horizontal plates separated by a distance l as shown in Fig. 1.3. The lower plate
is fixed and the upper plate is placed into motion in the x direction at a speed u
0
.
Viscosity forces the fluid particles in the layer in contact with the plate to move at
the velocity of the plate. Thus, at z
u
0
, and
at z = 0 the fluid is motionless. The force tangential to the upper plate required
to keep it in uniform motion turns out to be proportional to the area of the plate,
the velocity, and the inverse of the distance separating the plates. Thus, we may
write F
=
l the fluid moves at speed u(l)
=
=
µAu
0
/l where µ is a constant of proportionality, the
dynamic viscosity
coefficient
.
This force must just equal the force exerted by the upper plate on the fluid
immediately below it. For a state of uniform motion, every horizontal layer of
fluid of depth δz must exert the same force
F
on the fluid below. This may be
Fig. 1.3
One-dimensional steady-state viscous shear flow.
