Visualizing turbulence

Some mathematical order amidst the chaos of turbulence.
Vortex rings with Physics Girl: https://youtu.be/N7d_RWyOv20
Brought to you by you: http://3b1b.co/turbulence-thanks
Home page: https://www.3blue1brown.com

Thanks to Dan Walsh for many great ideas, and thanks to Mike Hansen for many helpful conversations.

Error correction: I meant to describe Kolmogorov as a “20th-century mathematician” not “19th-century”. Whoops! I think during the narration I must have made the classic 1900s vs. 19th-century mix up. Anyone aware of his work is more than aware of what century he lived in, which apparently applies to quite a few commenters.

And while we're here, the animation at 9:55 misleadingly has the vortex kind of speed up during the transition, which it should not do. Really, the velocity scales of eddies decreases for lower length scales.

Introduction to turbulence:
http://www.astronomy.ohio-state.edu/~ryden/ast825/ch7.pdf

More details on vortex stretching:
https://www.math.nyu.edu/faculty/tabak/vorticity.pdf

Video on NightHawkInLight with a similar demo:
https://youtu.be/K94Cc21KEIA

Music by Vincent Rubinetti:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

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Видео Visualizing turbulence канала 3Blue1Brown