Vortices and the end of Nemo

Well, that was a most unsatisfying end to a novel. After building up to an exciting conclusion, Nemo decides he’s had enough of wreaking revenge on his enemies* and plunges The Nautilus into the Moskenstraumen (Maelstrom) whirlpool off the Lofoten Islands, Norway, where, presumably, there is no return. (Or is there? I note there’s a sequel.)

Fortunately, Aronnax and his companions escape and survive the whirlpool (the question of  ‘how’ remains unanswered) and live to ‘tell the tale’.

Vortices are common phenomena in physics, specifically in fluid flow. We see them in water as whirlpools – a plug-hole vortex being a great example – and in the air notably as tornadoes and cyclones. But they also appear in other areas of physics, including electromagnetism and black holes.

Generally speaking they are tricky things to describe and there is a lot going on. One notable, and common vortex is an ‘irrotational vortex’. The terminology is confusing, for sure. A vortex clearly consists of rotating fluid so how can it be ‘irrotational’? It’s because the term describes not the way the fluid moves, but the way a particle in the fluid will move. Imagine I have some moving fluid (e.g. a river) and I throw in an object (e.g. a football). If the moving fluid causes the object to rotate, the flow is rotational. Note the fluid itself doesn’t have to rotate to do this. If the flow in the river was straight along the river, but quicker in the middle than at the sides, which isn’t unreasonable, what happens to the ball when we through it in? The side of the ball that’s closest to the centre of the river experiences a faster flow of fluid than the side that is closest to land. This difference in speeds on the two sides causes the ball to rotate. So a flow that isn’t rotating (the river) causes rotation in something that’s in it (the ball). Hence we can say the flow is rotational. 

It can work the other way around. A flow that is rotating does not necessarily cause rotation in a particle that’s in it. The irrotational vortex (like a plug hole vortex) is an example. Try this experiment. Set up a vortex in the bath. Throw in a test particle. (At home we use small bath ducks). The particle spirals around the vortex as it follows the flow, but, maybe surprisingly, it does not rotate. That is, if the duck is facing the front of the bath when you throw it in, it stays facing the front of the bath. There’s a neat little animation on Wikipedia showing this.

For a vortex to be irrotational, the speed of the fluid varies inversely with the radius. That is, 6 cm from the centre, the flow is half the speed as it is 3 cm from the centre. However, this relationship clearly cannot persist arbitrarily close to the centre – otherwise speeds get unphysically high. So, in practice, there’s a core to the vortex, where it becomes rotational. That might be the ‘eye’ of the cyclone, for example. The speeds drop off quickly, and, right at the centre, the fluid doesn’t move at all.

So, would the Moskenstraumen have crushed The Nautilus? Well, as you get closer to the centre of the vortex, the pressure gradients increase substantially. But, given that a couple of chapters earlier the submarine scythed its way through a battleship without any lasting damage to itself I imagine a truly vast Maelstrom would have been required…

 

*We never really get to know who Nemo’s enemies are, and why he is so opposed to them, hence part of my dissatisfaction with the conclusion. There are vague hints that it’s an oppressor state (perhaps France?, or Britain?), but if Verne wanted to make a political point in his novel he seems to me to have done it very obtusely.  But then what do I know? – I’m a physicist not an expert in literature.

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