# 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. Commented Feb 20, 2018 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. Commented Feb 20, 2018 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. Commented Feb 20, 2018 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. Commented Oct 10, 2018 at 10:56
• I think the deflection in a clockwise direction you are referring to is the deflection to the right. It won't keep turning that way, but when it meets air coming towards it, also deflected to the right, they will create an anti-clockwise vortex in the middle (the cyclone). See my diagram below. Commented Mar 22, 2023 at 1:33

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? Commented Apr 20, 2014 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. Commented Apr 20, 2014 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. Commented Apr 20, 2014 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.

• @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"!) Commented Feb 23, 2019 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.
– user1066
Commented Feb 23, 2019 at 7:43
• It seems confusing to call it minimal... as you say, it is a part of the balance. The stuff about coordinate system if I understand you, confuses people... you're saying is centrifugal caused by the cyclone's rotation (not from the Earth's rotation itself?)... and such: cdn.britannica.com/35/219435-050-461D1AD2/…. Thing is, you don't get this centrifugal force without a rotation start. So where is that rotation from in lowlat cyclones. Montgomery's VHT stuff (06) suggests a TD may develop from an insipient UL cyclone with planetary vorticity 0... but won't sustain Commented Mar 27, 2023 at 5:27
• So at some level Coriolis is needed... but not primarily. So you're not off. So then where does the rotation come from for the initial wave that builds a TC... for MCVs Conzemius&Montgomery (09) say "... the largest source of the positive PV anomaly in the MCV central region has to come from the flux convergence of absolute vorticity (the majority of which is planetary vorticity in the initial condition)". Of course there's other TC sources... e.g. mid-lat frontal systems likewise bring Coriolis-helped rotation to the tropics and grow. Commented Mar 27, 2023 at 5:34
• So point is... need an initial disturbance, and that does tend to involve previous Coriolis help. How does that rotation then grow? Then indeed centrifugal force grows in importance, and other mechanisms (first tilting and stretching of the initial vorticity field by local hot towers, then WISHE processes as the vortex grows). (Sorry, I should probably write this up into a full answer, but for now, since it stemmed from your answer and comment discussion, I'll go here... who has time these days!) Commented Mar 27, 2023 at 5:39

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.

• "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" this is not true. Even a wind or projectile flying directly east-west will be deflected simply by Coriolis, a little like how an object pushed tangentially along a record will not stay at the same radius. See earthscience.stackexchange.com/questions/14514/… here for some explanations, particularly Francesco's answer. Commented Mar 27, 2023 at 8:17
• @JeopardyTempest There would be some deflection due to the Eötvös effect, which is due to the increase, or decrease in centrifugal force pushing it toward the equator, but that has nothing to do with the Coriolis effect. I was going to throw in another small complication: Air moving towards the equator is slowly deflected eastward by friction with the ground. I was working out how to word it so I didn't confuse the poor guy, who, by now, probably wishes he had never asked the question in the first place. 😕 Commented Mar 28, 2023 at 4:52
• As far as I understand it, there is complexity/differences to what components folks include in Coriolis, so whether Eotvos is included within the Coriolis definition can be disagreed. Using the fundamental mathematical definition (such as given on the Coriolis wiki) that Coriolis is the cross product of the angular velocity vector to the relative velocity vector, Eotvos is one of the vertical terms I believe. Commented Mar 28, 2023 at 9:39
• However, that's an aside. Quite confident (though it gets plenty of challenge!) that the fundamental N-S deflection is an entirely separate term than Eotvos. See for example the diagrams at en.wikipedia.org/wiki/… ... "Coriolis parallel to surface" is entirely ⊥ to Eotvos. Commented Mar 28, 2023 at 9:41
• My apology to Kenshin. I should have said "the poor girl...." not "the poor guy....". I forgot to check the picture first, to get the gender right. Commented Mar 29, 2023 at 3:42