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I was watching a video on David Tong's research work when I stumbled upon a peculiar movement of vortex rings in water. Around the 1:20 time mark, Baths and Quarks: Solitons explained, David Tong uses an air-pump to create vortex rings in water. What I've observed was that the vortex rings go up and down in an ordered sequence (observe the attached pictures).

First shotSecond shotThird shot

As you can see from the attached pictures, the first vortex ring went down, the second one went up, the third one went down and the fourth one went up.

How can we quantitatively express this phenomenon? How can we mathematically understand this effect? Why and how does the inclination of the initial vortex ring effect the inclination of the vortex rings that come after it? Is the inclination (up or down) of the first vortex ring random or is it always downwards since there is an asymmetry in our problem due to gravity?

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    $\begingroup$ I definitely don't have an actual answer right now, but my initial guess is that is has something to do with how the previous vortex disturbs the surrounding water, and how that influences the next vortex. $\endgroup$
    – JMac
    Commented Jan 1, 2020 at 19:02
  • $\begingroup$ @JMac Do you know of any sources that treat this phenomenon? How would you approach the problem with the insight you have mentioned? $\endgroup$
    – user242231
    Commented Jan 2, 2020 at 21:02

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