Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

Fractal Flows and Tools for Tackling Turbulence

Audience:

Tags: physicsfluid-mechanicsturbulence

In this video, I introduce the topic of turbulence. I discuss what makes turbulence difficult to study, and I show how the scale invariance of turbulent flows (the fact that they look the same at different length scales) gives us a powerful tool to make progress in this field. I demonstrate the idea of scale invariance using examples, give a heuristic explanation for why it appears in turbulence, and then use it to quickly derive a famous result in the theory of turbulence.

Analytics

6.61 Overall score*
47 Rank
14 Votes
8 Comments

Comments

6.6

This is a pretty clever very well done video. I think this is more built for graduate student thought

8.3

Amazing video - production was top tier, explanations were clear, and it was very engaging!

Things I loved:

  • The quality of the animations and clips, and they felt perfectly aligned with the script.
  • Clear explanations and a good balance, you said enough to help people understand the topic without it becoming too bogged down in formulas.

There are only two things which could have improved it for me:

  1. The script could have motivated the viewer a little more - perhaps show practical examples to entice the viewer, with some clearer goals at the start of the video. (The WHY do we want to learn this?)
  2. Sometimes the formulas could have had more animation or visualisation to reinforce the true meaning of them behind the algebra.

Amazing job, and thank you so much for the upload!

6.6

The pacing is very good.

You probably shouldn’t bring up the butterfly effect, since it can lead people to a misunderstanding about chaotic systems, that if only you could find just the right small disturbance, you could create huge effects. Of course this isn’t true in general—dripping a small droplet of milk into the cup of coffee will never cause a powerful, hurricane-like vortex to form in the cup.

I wish you shared a bit of detail about how Eric made the simulation that you could keep zooming into!

In the recap at 19:28, it would have been good to say what P and k are, not “P and k”.

7.5

With this video I learned about the main features of turbulence. I didn’t know the property of scale invariance, which is very interesting and I suppose it might relate to fractals.

I really liked the tempo of the video because it enables you to follow the explanations without having to pause the video.

8.2

Students would find this video to be an outstanding introduction the the subject of turbulence. I was excited to hear about some unfamiliar concepts such as: enstrophy, stoke unit and dimensional analysis used in fluid dynamics. All in all very clearly motivated and animated, not extremely memorable. P.S. Fractals are spooky.

7.8

I think the problem statement of why turbulence is hard is good. If there were some physical systems that explain those that each part contrasts to, that might make it easier to get what kind of systems are difficult, but solveable. After that, it goes through an intuitive understanding of how we can still make sense of systems using some observations that did get the idea. I think I might be interested to learn more, and it would be good to leave more resources or tidbits on other techniques we could understand this better as well.

5.8

Clean visuals

6

good grpahics