Geoscience Reference
In-Depth Information
Radius, r
Angular velocity,
w
Latitude,
q
Figure 16.5
True speed of a
body along a line of latitude
relative to the apparent speed
when viewed from a frame of
reference fixed on the surface
of the Earth.
w
r
u
true
=
u
+
(
w
r
)
u
gravity acting toward the surface. Consequently, the axis-specific acceleration in
the Z direction required in Equation (16.6) is:
⎛
∂
w
⎞
=−
g
⎜
⎟
(16.25)
t
∂
⎝
⎠
axis specific
However, because the selected frame of reference is stationary on the surface of the
Earth, there are also axis-specific 'forces' causing acceleration, namely the X and Y
components of the
Coriolis force
which arises because angular momentum must be
conserved.
All bodies rotating around an axis have angular momentum that must be con-
served. The angular momentum of the body is defined as the triple product of the
mass of the body, multiplied by the distance from the axis around which the body
is rotating, multiplied by the speed at which the body is moving. Conservation of
angular momentum applies to the parcel of air at latitude
q
shown in Fig. 16.5 that
is constrained to move in a plane parallel to the surface of the Earth and that is
moving with an apparent velocity
u
in the X direction as viewed by an observer
who is stationary on the Earth's surface.
Because the Earth is rotating with an angular velocity,
, the true velocity of the
parcel as observed by an independent observer in space is:
ω
(16.26)
true
uur
=+ω
where
r
is distance between the parcel of air at latitude
q
and the axis of rotation of
the Earth. Angular momentum must be conserved in the frame of reference of this
independent observer and in this frame of reference the angular momentum,
G
, of
the parcel of air with volume
V
and density
r
a
is:
Γ=
(
Vu
r
)
(16.27)
a
true
