Geography Reference
In-Depth Information
from the axis of rotation to the object, the excess of the centrifugal force over that
for an object at rest is
2
R
u
2
R
R
2
u
R
2u
R
R
2
R
+
−
=
+
The terms on the right represent
deflecting
forces, which act outward along
the vector
R
(i.e., perpendicular to the axis of rotation). The meridional and
vertical components of these forces are obtained by taking meridional and ver-
tical components of
R
as shown in Fig. 1.9 to yield
Dv
Dt
u
2
a
=−
2u sin φ
−
tan φ
(1.11a)
Dw
Dt
u
2
a
=
2u cos φ
+
(1.11b)
The first terms on the right are the meridional and vertical components, respec-
tively, of the Coriolis forces for zonal motion; the second terms on the right are
again the curvature effects.
For synoptic scale motions
R, the last terms in (1.10a) and (1.11a) can be
neglected in a first approximation. Therefore, relative horizontal motion produces
a horizontal acceleration perpendicular to the direction of motion given by
Du
Dt
|
u
|
Co
=
2v sin φ
=
fv
(1.12a)
Dv
Dt
Co
=−
2u sin φ
=−
fu
(1.12b)
where f
≡
2 sin φ is the
Coriolis parameter
.
Fig. 1.9
Components of the Coriolis force due to relative motion along a latitude circle.
