Coriolis effect and Cyclones

Question

The Coriolis force predicts that winds in the northern hemisphere should be deflected in a clockwise pattern and winds in the southern hemisphere should be deflected in an anti-clockwise pattern. Why is it that in the case of cyclones however, the cyclones spin anti-clockwise in the northern hemisphere and clockwise in the southern hemisphere?

Answer 1

Don't think of the Coriolis force as deflecting motion clockwise/counter clockwise, but to the right (NH) or left (SH), when looking in the direction of the motion.

So this is sort of 'by definition'. A cyclone is a low pressure system, and air will move from a location with high pressure towards a location with low pressure. The Coriolis force will deflect this air to the right in the Northern Hemisphere, creating a counter-clockwise motion around the low pressure. Around high pressure systems the direction of the motion is opposite, anti-cyclonic.

A very simple sketch, with a low pressure in the centre, and higher pressure around it:

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Another way of looking at this is through the equation for geostrophic motion. The wind around a cyclone is (nearly) geostrophic, so the equation of motion can be simplified to

$$ f\mathbf{k}\times\mathbf{v} = -\frac{1}{\rho}\nabla p $$

where $f$ is the Coriolis parameter, $\mathbf{k}$ is the vertical unit vector, $\mathbf{v}$ is the wind speed vector, $\rho$ is density and $\nabla p$ is the pressure gradient.

So, looking at a sketch of a low pressure system on the northern hemisphere, the pressure gradient force will look like

The gradient itself goes from low to high pressure, but the force has the opposite direction. To achieve a balance between this and the Coriolis term, we need this situation:

(Note the negative sign for the Coriolis term here. In the above equation we have equality, so with the negative sign the direction is opposite that of the pressure gradient force.)

As $f$ is positive on the northern hemisphere, when we use the right-hand rule for cross-products, this means that $\mathbf{v}$ must be directed as

i.e., giving a counter-clockwise motion around the low pressure.

Answer 2

To correct your phrasing slightly: The Coriolis force acts to turn flows in the northern hemisphere to the right. This is not quite the same as "in a clockwise pattern", as will become evident in a moment.

Cyclones have a low pressure core and higher pressure outside. Therefore, the wind is flowing from the outside in.

When we think of a cyclone, we think of a fully-formed one that has a spiral pattern. If one sets out to draw a spiral from the outside in, and bears in mind northern-hemisphere Coriolis, one curves it to the right and ends up with a clockwise spiral, which is wrong:

However, a cyclone doesn't start out this way. Instead, think of a low pressure area inside a higher pressure area, so that the wind is blowing towards the centre from all directions. Draw a number of radial lines to show this... and then curve each of those to the right:

Note that the resulting circular motion (blue arrows) is counter-clockwise.

Now, AIUI a cyclone doesn't quite start out that way either, but I hope that this simplified approach explains how the "wrong" direction of rotation could be produced.

Answer 3

As the earth rotates, when air moves from near the poles towards the equator, the radius of that part of the earth is larger, which means, the ground is moving faster and the air lags behind. When the air is moving from near the equator towards the poles, it travels to where the radius is smaller and ground speed lower, so the air races ahead, causing a cyclone in the southern hemisphere to rotate CW, and one in the northern hemisphere to rotate ACW. The Coriolis Effect will not affect the direction of air from the east or west, but it will be deflected by the vortex, and then help to push it around. (Any fluid approaching a common point, like a thermal up drought, or drain hole will tend to form a vortex, but the Coriolis Effect will decide which way, if the vortex is big enough). All cyclones have lower pressure inside due to the centrifugal force from the air turning, which keeps it going in a circle like a tornado, but not as concentrated, although the people in Darwin might disagree after Cyclone Tracy on the night of Christmas Eve 1974. The place looked like Hiroshima after the bomb.

Incidentally, the Coriolis Effect is not a force. The air is just continuing roughly in a straight line like it was (ignoring ground friction, which slowly deflects it the other way), but the ground speed is different in different places, so, from the ground, it appears deflected until it gets into a vortex, where it actually is.