How does the Coriolis acceleration affect flows?
It's a really interesting phenomenon known as geostrophic motion.
Imagine that you have some push force.
This could be high pressure on one side of a column of gas, and
low pressure on the other, or it could be
wind blowing over the surface of water and tending
to push the water in some direction.
But what the water does initially, if you push it
in some direction, is it goes in that direction.
In the same direction as you push it, and when it starts going in that direction,
you produce a Coriolis acceleration, which is always going at 90
degrees to the direction that it's moving. What this is acting to do
is pull the direction of the flow around, to rotate it.
The same way as the direction of the ball
in the merry go round was deflected by the Coriolis acceleration.
After a little while, the flow is not going the
same direction you were pushing it anymore; it's rotated.
Off to the side, and the Coriolis is always following the flow here,
and eventually you end up with the equilibrium state, which
is what it relaxes to and then stops changing.
It can stay in this equilibrium state forever, where the flow is actually
astonishingly going at 90 degrees to the
side of the way you're actually pushing it.
And in this way, the Coriolis, which is 90 degrees
to the flow, is now pushing back, exactly counteracting the push force.
And so that's why this is equilibrium,
because those forces can cancel each other out.
You can't even look at a weather
map without seeing the affect of geostrophic motion.
A hurricane is basically a hole in the atmosphere where the
pressure is lower, the atmospheric pressure, than it is in the surrounding air.
You remember that the pressure is just the result of the
weight of the air on top of you head in the atmosphere.
This low pressure at the ground at the center of
a hurricane just means that there's less air piled up there,
and the difference in the air pressure is leading
to a push force going from high pressure to low pressure.
You would think in a non-rotating frame,
if you had higher pressure of gas here and
lower pressure there, it would just go from the high
pressure to the low pressure and fill in the hole.
But due to the geostrophic motion, you have the
flow in the atmosphere is going at 90 degrees to the way you're pushing it.
It's going around like this.
And then the where, where the flow is going in this direction.
The Coriolus is
pointing at 90 degrees to that and so the coriolus is reaching
the state of equilibrium, where it's pushing
back against the push force, in the geostrophic equilibrium.
It is as if you made a hillside.
Or, a dip in a membrane or something like that.
And you set a marble on it.
And in a non rotating frame, it would just roll to the bottom of the hill.
But in a rotating frame, it doesn't go the way you're pushing it.
It goes sideways to it, and so it goes around
and around and around, only very slowly does it go down.
And this is why hurricanes last as long as they do.
There's a feature on Jupiter called the great red spot.
Which, as far as we know, has been there for centuries.
And it's just one of these sorts of
systems with a pressure imbalance and the flow
going around and around and around in geostrophic motion.
And that's why it can last for so long.
You also see the effect of geostrophic motion in ocean flow.
The gulf stream is a giant river of water in the North Atlantic.
And the sea level is about one meter higher on one side of the Gulf Stream
than it is on the other.
It's very wide feature so you never see a wall of water a meter high.
It's too spread out to be that obvious.
But, you can measure it, and if you measure also
the pressure at some level underneath the ocean level,
you have higher pressure here where the sea level is higher because
you have more stuff over your head than you do here
where the sea level is lower.
You have a pushing force going in
this direction, and then in geostrophic motion, you have the Gulf
Stream which is an arrow going into the board
here, 90 degrees to the direction that you're pushing it.
In order to simulate, the way that the atmosphere and the ocean carry heat
from the low latitudes to the high latitudes, we have to understand about
how flow occurs on a rotating sphere.