Geoscience Reference
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hemisphere it acts to the left. In
Box 3.2
we demonstrate how the Coriolis force arises
in the particular case of a particle of water traveling due east.
The vertical component of the Coriolis force, 2
O
u cos f
L
, is generally very small in
10
5
g) and other forces acting in the vertical and may
usually be neglected. Why then do we have to include the horizontal components
which are of the same magnitude as the vertical component? The answer is that the
Earth's gravity has, by definition, no component in the horizontal and the other
horizontal forces acting (e.g. pressure, frictional and tidal forces) are generally much
smaller than g and of comparable magnitude to the Coriolis force.
comparison with gravity (
∼
Box 3.2 Coriolis force
Consider the acceleration of a particle moving due east on the Earth's surface at latitude
f
L
as in the figure below. We wish to know its absolute acceleration; i.e. our viewpoint is
that of an observer in a non-rotating frame of reference. The particle has an eastward
velocity u relative to the Earth. Its velocity, as seen by the observer, is the sum of u
and the velocity associated with Earth's rotation at the particle's position, which is just
u
rot
¼ O
a
E
cos f
L
where a
E
is the radius of the Earth and
O
is the rate of angular rotation.
N
(a)
(b)
Ω
Radial
acceleration
u
u
a
E
cos
φ
L
φ
L
Figure B3.2
The radial acceleration of the particle moving in a circle in the non-rotating frame is
U
2
¼
þ O
¼
r
where U
u
a
E
cos f
L
is the total speed of the particle and r
a
E
cos f
L
is the
radius of the circular motion, i.e.
2
U
2
r
¼
ð
a
E
cos
L
þ
u
Þ
:
a
E
cos
L
Expanding the right side of the equation we see that the total acceleration consists of
three components:
u
2
a
E
cos
2
a
E
cos
total acceleration
¼
L
þ
L
þ
2
u
:
The first term is the centripetal acceleration of a fixed point at latitude
f
L
as it rotates
around the Earth's axis, while the second is the centripetal acceleration of a particle
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