Environmental Engineering Reference
In-Depth Information
ω
2
. This is of course a major
this implies, using the second equation, that
v
2
∝
simplification and we get
ωgt
2
v
1
≈
cos
λ.
(8.31)
The bottom line is therefore that a particle dropped from rest relative to the Earth
will not fall directly towards the centre of the Earth but instead will be deflected
slightly to the East. Like the motion of the ball on the turntable, this is not too hard
to understand. The easterly direction is special because it points in the direction
of the Earth's rotation, as can be seen in Figure 8.4. A ball dropped from a height
above the ground must move this direction because, at the instant of release, its
speed in the easterly direction (as viewed in an inertial frame) is too great for it to
fall only along a radius vector. As a parting remark, you might like to see if you can
convince yourself that the neglect of terms quadratic in
ω
is a good approximation
if
ω
2
R
g
and if the total time of the motion is much less than 1 day.
Secondly, we shall consider the case of an object moving horizontally on the
Earth's surface. In this case, we know that
v
3
=
0 for all times and the motion is
in a plane. The Coriolis acceleration is just
1
m
F
Cor
=
2
ω
sin
λ(v
2
e
1
−
v
1
e
2
).
(8.32)
The general situation for motion in the northern hemisphere is illustrated in
Figure 8.6 and it shows the Coriolis force acting in the direction of the vector
−
ω
×
v
. In the northern hemisphere sin
λ>
0 and the object is always pushed to
the right. In the southern hemisphere sin
λ<
0 and the object is pushed to the
left. At the equator sin
λ
0 and there is no Coriolis force. It is a consequence of
the Coriolis force that large bodies of air do not move in straight lines around the
Earth. In the northern hemisphere the air swirls in a clockwise direction as viewed
from above whilst in the southern hemisphere it swirls in an anti-clockwise
direction. Cyclones are regions of low pressure and as such the air around the
cyclone moves towards the centre. As it moves it is deflected as a result of the
=
x
2
(N)
Northern hemisphere
v
F
Cor
(E)
x
1
Figure 8.6
The Coriolis force acting on a body moving in the northern hemisphere.
