# Coriolis effect and Cyclones

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?

• The easy way I find to remember which way they spin is that cyclones spin the same way as the ground (clockwise in the southern hemisphere, anticlockwise in the north), while anticyclones spin the opposite way. Feb 20 '18 at 0:46
• Does anybody else get annoyed with TV weather animations that show the wind vortices spinning like crazy? Each revolution has to take at least one day, if not longer. Feb 20 '18 at 0:48
• It's a classic case of (required) flipping of perspective. Gravity makes things move down... unless you turn upside down yourself, in which case it makes thing move "up". A high pressure, the wind moves outwards from it, all positive directions, so turning right (NH) = clockwise. But a low pressure, wind moves in... that's a flip of perspective... so turning right = counterclockwise. Feb 20 '18 at 4:47
• Thank you, Semidiurnal. But i think you've got this one wrong. Cyclones act as turbulent geographical entities which disperse along an equatorial gradient shown by the simple equation: F= 7op;']#1 X y09990 And now you know. Oct 10 '18 at 10:56

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:

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.

• Thanks for your answer. Torbjorn, why does nature want to balance the coriolis effect with the pressure gradient? That is, why does nature adopt the geostrophic pattern in the first place, that leads to the equation you typed? Apr 20 '14 at 11:18
• @Mew Very briefly, to get the equation for geostrophic motion, you start with the complete equation of motion, assume large scale motion, that friction is negligible (you're away from the ground) and that |f| > 0 (you're some distance away from the equator). Then you do a scale analysis inserting typical values, and remove the smallest terms. What is left is the above equation. That is of course just an approximation, so geostrophic wind (or current, in the ocean) is defined as that wind/current speed where the Coriolis force balances the pressure gradient force. Apr 20 '14 at 11:58
• @Mew Geostrophy is just an approximation, but it is a quite good approximation. Also, in a non-rotating system, the equilibrium state is one where the fluid (air, water) is at rest, while in a rotating system, the equilibrium state is one of (geostrophic) motion. Apr 20 '14 at 12:06

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.

• old answer yes but some other perspectives as well. The Coriolis force is minimal at such low latitudes where cyclones form. The cylostrophic balance is a balance between pressure gradient, centrifugal force and Coriolis force. The primary circulation in a cyclone (which is the swirling wind) is primarily due to the centrifugal force. Feb 23 '19 at 3:46
• @gansub I'm sure you're right, but (assuming you mean the centrifugal force from the cyclone's rotation rather than that from the earth's rotation) surely that would work equally well regardless of the direction of rotation? (a heavy caveat here of "not my field"!) Feb 23 '19 at 6:37
• @SemidurnalSimon - it is everybody's field as nobody is really an expert. This is just a conversation. :-). No I meant that in a global coordinate system it is from the earth's rotation and hence centrifugal. In a local coordinate system the centripetal force :-). So the question is what keeps it rotating anti clockwise and my point was a balance between pressure gradient and centrifugal force + Coriolis. The question on the RHS (centrifugal force and Coriolis) is which term is greater. My point was centrifugal. Feb 23 '19 at 7:43