Geography Reference
In-Depth Information
a cos φ, where
a
is the radius of the earth and φ is latitude,
dividing through by the time increment δt and taking the limit as δt
Noting that R
=
→
0, gives in
the case of a meridional displacement in which δR
=−
sin φδy (see Fig. 1.8):
Du
Dt
2 sin φ
a
tan φ
Dy
u
uv
a
=
+
Dt
=
2v sin φ
+
tan φ
(1.10a)
and for a vertical displacement in which δR
=+
cos φδz:
Du
Dt
2 cos φ
Dz
Dt
=−
u
a
uw
a
=−
+
2w cos φ
−
(1.10b)
where v
Dz/Dt are the northward and upward velocity
components, respectively. The first terms on the right in (1.10a) and (1.10b) are
the zonal components of the
Coriolis force
for meridional and vertical motions,
respectively. The second terms on the right are referred to as
metric terms
or
curvature effects
. These arise from the curvature of the earth's surface.
A similar argument can be used to obtain the meridional component of the
Coriolis force. Suppose now that the object is set in motion in the eastward direction
by an impulsive force. Because the object is now rotating faster than the earth, the
centrifugal force on the object will be increased. Letting
R
be the position vector
=
Dy/Ddt and w
=
Ω
φ
0
R
0
δ
R
φ
0
R
0
+
δ
R
φ
0
φ
0
+
δ
φ
Fig. 1.8
Relationship of δ
R
and δ
y
=
a
δφ for an equatorward displacement.
