What are coriolis
forces?
This page supports the multimedia tutorial Newton's Laws
Coriolis forces – what are they? And why do the large scale winds and
ocean currents move clockwise in the Northern hemisphere and anticlockwise in
the Southern hemisphere? This is a simple, non-mathematical explanation.
There are links to related material below.
Imagine that you fly a hot air balloon, starting at Sydney. Further, let's
imagine that an astronaut on the moon is watching you. As it happens, the wind is
going due South, according to your compass. You check your GPS and, sure enough,
you latitude is increasing and your longitude is (for the moment) staying the
same: you are travelling South – with respect to the earth.
 Meanwhile, the astronaut on the moon can see that the Earth is rotating, and she
sees both you and Sydney travelling in a circle around the Earth's axis.
(Her view is shown at right.) The rotation of the Earth means that both
you and Sydney are travelling towards the East at about 1400 km/hr. The
inhabitants of Sydney cannot feel this motion, partly because everything
around them except the moon, stars etc is moving, and partly because the
motion is smooth (i.e. very little acceleration is involved). In your frame
of reference, you are going due South, with no Easterly component of
velocity, but the astronaut knows better.
Imagine that you continued travelling with the same South and East components of velocity (as viewed from the moon). What would happen? Well, by the
time you get down to the Southern Ocean, you will be over a point on the
Earth that, according to the astronaut on the moon, is still travelling East,
but a speed of only 700 km/hr. So, if somehow you still had the Eastward velocity you had when you were above Sydney, you would now be travelling 700km/hr faster than the Earth in an
Easterly direction. In other words, you would be travelling mainly East!
Your path would be a little like the thin line on the diagram: you headed
South from Sydney, but you turned left, and you are starting an
anti-clockwise motion.
We could reverse the argument for a balloonist travelling North along
the West coast of South America. This surprised tourist will arrive at the
tropical latitudes to find that the Earth is travelling East much faster
than he is. In other words, relative to the Earth, the tourist is
travelling West. Again a left turn, and again anti-clockwise motion. (Thin
line at right of diagram.)
So the winds (and the ocean currents) in the South Pacific go mainly
anti-clockwise: South along the East coast of Australia, East across the
coast of Antarctica, North along the West coast of South America, and then
West across the middle of the Pacific.
But what made you turn? Well, according to the observer on the moon, it was
more a case of the Earth turning: viewed from the South, the Earth's
rotation is clockwise. The surface of the Earth is turning, and turning
means changing direction, and changing direction means accelerating. In an
accelerating frame of reference such as the surface of the Earth, Newton's
laws don't work. In order to make them appear to work, we can invent
fictitious forces. The name of the fictious force that appears to have
caused you to turn is the Coriolis force.
In the case of the surface of
the Earth, the acceleration is very small, because the rotoation rate is
very slow - only slightly more than one turn per day. So, the
approximation that Newton's laws hold on the surface of the Earth is good
enough for most applications. To see the error in Newton's laws as applied
to this frame, one needs a carefully set up, slow experiment such as a Foucault
pendulum.)
It is important to remember that centrifugal forces and Coriolis forces
are purely fictitious, they are artifacts of making measurements in a frame
of reference that is accelerating. However, the surface of the Earth is an
extremely convenient frame of reference: any observing instruments that
are in an inertial frame disappear from the view of an Earth-based
observer rather quickly! So, for convenience in measuring and analysing
motion on the Earth, we often use the Earth-based frame of reference. (To
see how much convenience is gained, you might like to try doing a simple
ballistics problem in inertial coordinates and then relating the result to
a coordinate system on the surface of the Earth.)
See the
principle of relativity for more detail and the site on the Foucault
pendulum for related information. |
A footnote: Does the rotation of the earth affect the way in which water runs
down the plug hole when you empty the bath? Some people say that the water
goes down clockwise in the Southern hemisphere and anticlockwise in the Northern
hemisphere. Such people have probably never, or very rarely, looked. In some
bathtubs (or basins etc) and under some conditions, the water runs out
clockwise, in others it runs out anticlockwise. There is no correlation with
the hemisphere. Other effects may lead to the direction of draining. For
instance, some basins have separate cold and hot water taps that are positioned
symmetrically left and right. If you fill the basin using the left hand tap, you
set up a rotation in one direction, and this will determine the direction in
which it drains. Using the other tap reverses the direction. Many basins and
baths are sufficiently symmetrical that it is possible, with some care, to have
the water drain with no observable rotation. Alistair Fraser has a page devoted
to silly comments
about Coriolis forces and water in basins.
Every now and then, someone (usually from the Northern hemisphere) writes to
tell me that they have checked the bath, the sink, the hand basin and the
laundry basin and that all of them drain the same way. Now, in either
hemisphere, the chance that a basin drains clockwise is about 50% (unless you
drain it carefully enough to have no rotation at all, which requires a bit of
patience and thought). So, with four basins/ sinks etc in a typical house in a rich country, there is a 1 in
16 chance that they will all drain clockwise, and a 1 in 16 chance that they all
drain counterclockwise. So about 6% of people would get the result that all
their basins drain in the direction of cyclones in their hemisphere, and another
6% would get the result that all drain in the opposite direction. Perhaps the
people who write to me are from one of these groups. However, I rather suspect
that some of them have never looked, or never looked more than once or twice.
Rather, I think that they have been told this, have stored it away as a 'fact',
and are really upset to discover that it is not a fact.
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