3Blue1Brown - 2018-11-07
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 ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown
I got to see a lot of this footage in person, and it somehow looks better with Grant's tranquil voiceover. A+
Ok......Sebastian ...
@Paul Thompson I second this!
Hey physics girl what's your real name
Make the vortex stand in place. Sucking it backward or blowing it from the front, or both combined, could maybe do the trick.
I see an analogy with the Lorentz force, visualizing this. Maybe wrong maybe not.
Hear me oh Great 1.
I wrote my doctoral dissertation on optical probes into fluid turbulence. Using proper beam paths and correlation functions, it is possible to directly measure the Kolmogorov scale in real time. I'm really happy to see this video because there is so much fascinating and important physics and mathematics to be found in fluid turbulence.
Joseph D. Harris, thank you for sharing! I found your PhD thesis: https://drum.lib.umd.edu/bitstream/handle/1903/11461/Harris_umd_0117E_11928.pdf?sequence=1
@Joonas Mäkinen Thank you for looking me up!
Really nice summary. I'm a beneficiary of all that theory in my career as a civil engineer working on dam spillways and hydraulic structures. For complex projects, we still build scale physical models because even the CFD software doesn't do a great job predicting turbulent flow conditions.
Thanks for the replies. What you wrote it is true and i agree with you. I just wanted to point it out that even les is based on "historical" assumptions that are now in serious doubt (for example the 5/3 law dealt with in the video it is tought now to not hold, at least in the way kolmogorov intended)
I really love that so many of my favorite YouTubers interact like this. :) I don't subscribe to a lot of channels, but I am an enthusiastic subscriber / supporter of 3B1Br, Physics Girl, AND Practical Engineering. Please keep it up, guys!
Could it be that straight motion in higher dimension create circular in lower?
CFD can do insanely good job in most situations, if the right models are used for the right applications, however, most engineers don't use them properly. A hammer can't be used properly to screw, but it doesn't mean that it's a bad tool.
Lewis F. Richardson is my new favorite poet. Who says art and science don't mix? Leonardo is my cousin.
Please make Navier Stockes in depth
I had like 1 year in Uni about that equation. Trust me guys its screwed up^^
@FoolWise understanding how to use the equations and what they mean is actually pretty simple
@Nate Werner Well, to me it's like the Schrödinger Equation. Simple in principle, complex in application.
Measure theory does fit this channel better.
Just become a chemical engineer. You'll have plenty of fun with this stuff.
"high swirly-swirly factor" <- perfect
Which is, of course, distinct from the swirly-whirly factor
Cried from laughing at this.
And that's how fluid dynamics do.
@Todd Starbuck that sounds familiar to me hahaha
True Facts about Tyoorbulance
Another thing about green lasers: Do not buy cheap green lasers!! They do not radiate pure green light - in the worst case the biggest part of their radiation is in the infrared spectrum. You will not even know how strong this light is, and it can blind you in no time. More expensive lasers filter this infrared part out, or use more efficient ways to create green light - ways that don't produce the "byproduct" infrared light.
Just to make sure this was said and everyone who wants to try, knows.
I have a laser pen(2 of them ,actually) that emits blacklight UV, it makes bleached cartridge paper and anything "Hi-viz" glow very brightly. Would that work better than green
?
@Dudley Middleton I personally wouldn't know, so maybe you can Google away for the safety specifications :)
The IR emissions are not a byproduct being produced, it's the raw output of the diode before it's doubled by a crystal to the good old 532nm lime green we all know. Good lasers aren't avoiding production of byproduct, they're simply doing a better job converting the raw output to the desired wavelength + using filters to prevent any leakage of of the IR.
@thefunkybside in other words a byproduct
Any recommendations for a good model?
"When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."
-Werner Heisenberg (maybe)
Horace Lamb. Misattributed to Heisenberg, because of Heisenberg's interest in turbulence. Heisenberg also found the Kolmogorov laws in the late 1940s.
Fluid dynamics ftw! You absolutely need to make a video on the Lorenz system and strange attractors!!
Maybe you can give him some piano background music...
Yeeeesssss
Everybody like this so he sees it!
my Probability Theory professor was Kolmogorov's PhD student, pretty sure Kolmogorov was not 19th century :)
Who was your prof? Gelfand? Arnold? Martin-Löf? Uspensky? Dynkin? ...
(Kolmogorov apparently had no time for advising non-genius students.)
Well you are right, he was 20st century. Showing once more how late stochastics was made senseful
My Econometrics professor was Kolmogorov's student in MSU, he is always proud to mention he was taught by such a great mathematician.
@Arman isajanyan I'm just responding to this because I am an MSU student as well, and I think this is cool. I believe this is my first comment on YouTube, you should feel special ;)
My math phobia is over. Grant, you are the bees knees.
Awesome!
I cant wait to get a job and support you on patreon. Sometimes it feels like I am just a selfish person learning so much incredible things from you. :(
Just in case anyone's not aware, you can support 3B1B from just a dollar or 2 per video. It doesn't have to be a big commitment.
Woah, nice to see you here bro!
You deserve huge respect for your hardwork....for such crazy animations...
"Diana's typical and infectious, superhuman level of enthusiasm" so accurate lol
Everything about this is oddly satisfying
No, just leave
welovfree Hello sabo, have you been reading the manga lately?
What's odd about it?
@Science Compliance "oddly satisfying" is a well know topic on Reddit, and that's what welovfree was referring to
And here I thought I was going to learn something. And instead of something that my small brain can grasp, You challenge us with Navier-Stokes Equations ;)
Thank You, although I hope that You will someday make essence of Probability, or if You are going with fluid dynamics, the essence of it.
EDIT: Also before watching Physics Girl video: The corners of square will make additional vortexes, and it will depend whether the square is smaller or bigger than the circle, so these Vortexes will have either positive or negative pressure. That's a prediction - I'm very bad at fluid dynamics.
EDIT2: After Watching Physics Girl Video (SPOILERS): I knew that corners might do something (duh), I thought they would be the points where it breaks. It probably does, but only after main Vortex loses enough energy (by just traveling + by wobbling), then they are the weakest points. I wonder if for a moment you have 4 almost linear, and disconnected vortexes?
I just gotta say, im a phd student studying computational fluid dynamics and turbulence and I showed this to several of my lab mates and we all absolutely loved it!! ty for making this somehow both accessible to a broad audience and still true to the complexity of the subject matter, its not an easy feat and this video does it very well!!!
Same. I did something relating to boundary layer separation for the Science and Engineering Fair of Houston and analyzing turbulence with CFD is one of the most important parts. This video truly helped me with the CFD parts of it.
"Eddies in the time space continuum"
"Ah, is he?"
Yes. That's his sofa!
No no no, you don't get to cut the video there. You haven't explained many things, I need knowledge!
hey Grant, awesome video as always! here something a little less known but absolutely fascinating you might appreciate : "Lagrangian Coherent Structures"...look for the paper by prof george haller, i think its free on his homepage. mathematically its pretty amazing already (geodesics etc) but then they are able to identify transport barriers on ocean surfaces etc, predicting what swirls will remain stable over a longer time!
3:55 "swirly-swirly factor"
Is that a real technical term, or is it just you trying to make me giggle? (Because you succeeded)
why does the laser plane look lenticular after passing through the glass rod?
india atkin Probably because it doesn't disperse the laser linearly with respect to angle when projected on a plane. The wavefronts of the photons sweep out a curved path through space, not a linear one.
Physics Girl sent me here and now I'm guided back there. Alone the idea to create a planar laser "blade" is so fascinating I could loop through these two videos for some more iterations.
Wow, that's cool. When I was an engineering student in fluid dynamic our professor told us the partial differential equations that describe fluid dynamics are unsolvable and what we had to do was make simplifying assumptions that would linearize the equations. Then we could use our ordinary calculus and matrix math to solve the problem.
The Navier-Stokes equations are solvable. There are about ~200 known exact solutions to them actually. The issue with the NS equations is that they aren't guaranteed to be solvable due to their second order nature (which comes as apart of the viscosity term).
The cases where they are analytically solvable are very simplified, with very simple geometries and typically neglecting either compressibility or viscosity (or both).
Any higher degree of complication can only be solved numerically, and even then with simplifications needed to make it practical. For example CFD is a numerical way of solving these equations, but CFD does not solve the N-S equations directly. It applies turbulence modelling (therefore simplified) and solves the rest.
DNS is a direct numerical solution of the full N-S equations, but no computer in existence is powerful enough to do it for any type of practical problem, so it is only used for very simple geometries, and not very high Reynolds numbers, mainly as a research tool.
this is also a cross-sectional view of the magnetic field of a conducting metal ring lol
Small typo in the technical note at 8:43, “eddy’s” instead of “eddies”.
This is by far my favourite YouTube chanel. I really appreciate how you make videos talking about mathematics on such a high level, with so much enjoy and really well done animations. Math is something that I love for basicly my whole life, but I never loved as much as I do now thanks to your chanell. Thank you for making every single video here on youtube. :)
Ps: I'm from Bazil, and english is not my first languege, so sorry about any grammar mistake or stuff.
6:43 Andrey Kolmogorov was born in the 20th century, not 19th ^^
I see 5/3 I think golden ratio. Has anyone tried to see what happens when the exponent is phi?
Well, actually 5/3 evaluates to 1.66666 compared to phi which is 1.618033. There is a 3% difference. I think you are one of those rabbit counting Fibonacci people. While Fibonacci is a great approximation of phi, it only works when it sets to large numbers. One day I graphed y=x^phi on www.desmos.com then I made a separate table for Fibonacci numbers and played around with it.
alan makoso
lucas numbers are the true phi
i remember when i derive the in-compressible from of the equation, my teacher give me an evil eye and tell me to slow down.
thank you sir, i was working with navir stokes equations lately, i hop you read my message, please do a video about that equation
“Superhuman lvls of enthusiasm” nailed it 🤣
Just the thumbnail gives me a great idea for a homemade, scale-sized wind tunnel.
With that opening music, a Pavlovian-trained voice in my head said, "Look around you. Maths."
The new opening animation looks great.
Mmmm... I love this! Ever since I was able to recognize that I had thoughts I saw this 'chaos' as beautiful patterns. Nothing is ever the same as something else. You don't see the same sunset as I do; I am sitting to your left and I have you in my peripheral vision and on my mind and I feel a shoulder on the right side of my chest while I have my arm over your other shoulder. You do not. My molecules share a history with yours, but ever so slightly different. The path for every particle to where it is now is different and all combinations are unique, despite obeying the same natural laws. Those natural laws are what bind us, the paths are unique.
Another example: The branch of a tree doesn't 'happen' to be there and have that shape and color and composition. It's the result of genes, wind, sunlight, temperature of the ground and surrounding air, nutrients, water, how much of which was where at what time in what combination and the damage and help that other flora and fauna gave it. All of those are unique, not just for every tree or branch but for every cell and cell division, giving each tree its own unique 'character', showing it's entire history, all the interactions with all life around it and all particles, the climate, the weather.
Take a step back and look at the species as a whole and how it developed through time with changing climate and surrounding flora and fauna. Take another step back and see how the planet formed. Step back and see the universe too shape. All the way back to just after the beginning when hydrogen was all there was. - That picture of the background radiation is the earliest baby picture of all of us together that we have; think about that for a second -
Every leaf and every branch is a logical result of all of our histories and every particle has its own history that's interconnected with other particles. Every human has their own history that is interconnected with everything else. We're not random, we're a logical result. We're not chaotic either, we are a logical result. Hard and often impossible to predict, yes. There are too many variables for accurate predictions. We simply don't have and probably will never have perfect knowledge of the initial conditions. That's also why we still have the relative freedom to make decisions and the responsibility to gather information to make the best possible decisions, while most likely being in an absolutely deterministic universe, where true chaos simply cannot exist.
All patterns are simply the logical result of our history and I don't know if the laws of nature are a part of that history or only a cause of it. Maybe there are other universe where at the beginning something was different that resulted in different laws of nature and possibly some of those laws couldn't work and the universe collapsed and some worked well and went on existing. Who knows? What we do know is that the laws of nature in this universe made everything to be the way it is now, including your thoughts at this very second.
The history of the entire (visible) universe (and to a lesser extent that of what is not visible anymore but once was connected to the part of the universe we are causally connected to) is in everything you see and think. The entire history of the universe and the history of the person, including everything they ate and the love they received is in the colors and the seemingly chaotic, but definitely unique patterns of the iris of the person you love most. What that history looks like is a mystery, but it is definitely there. You now know the color of the eyes of the person you love and where the specks are in the iris of the person looking back at you. Now take a step back in your mind and look at how you're interacting with each other and at what you want to do next. Your future is as unique as your history. Choose something. Choose a general direction you want to pursue and choose an action as a step on the path in that direction and do it.
I'd love to have an explanation on the intuition behind this 5/3 mystical formula. Maybe a future video?
5:38 if the equation for an incompressible gas is hard to understand I don't want to imagine what's used for compressible gases.
You are a living "Richard Feynmann" for us.... The way u simplify ur explanations is amazing
"High swirly swirly factor" made my day😂
loved the video. finally can give my friends an idea of what i‘m doing.
just a minor correction:
you said „when something compressible like air“. compressibility is not a property of the fluid but the fluid flow.
What a pleasure to see my dearest curly branch of maths here! Kolmogorov 6:41 has definitely lived in 20th century, though.
I vow to call fluid dynamics curly math in any and all enviorments.
Love the visualizations done by Physics Girl; in the fluids world this is almost identical to an experimental technique called stereo particle image velocimetry (PIV). With PIV more distinguishable particles are suspended in the flow and imaging used to find a vector field at each time step recorded.
8:52 "zero point one centimeter", also known as "one millimeter"
A whole series on fluid dynamics would be so cool :)
Hi! What is the meaning of ' Quantifying energy held at different length scales in terms of Energy Spectrum'?
3Blue1Brown : I first thumb up, then watch. :-)
Same:-)
That's not very scientific. :P
@NoLlama It's very scientific : all the experiences (the other videos) have shown that his videos are the best in the world. So it's almost certain that this video will be amazing.
So you have a hypothesis that all 3b1b videos are best. You've build a theory which makes a prediction that all future 3b1b videos will be the best as well. And the videos keep coming and they're the best and you mark it with a thumbs up every time your theory makes a correct prediction. So you may think "That's it, that's how it works". But then this guy comes in and figures out that your theory only works under certain conditions but is torn to tiny pieces in more extreme conditions no one's going to experience ordinarily. And the guy's name? Albert Einstein.
And so that's why we all have to constantly put even our most rigorous theories to test and why I'll always watch the whole 3b1b video and only then give a thumbs up, because I believe in the scientific method!
I really don't know where I was going with this comment... but it was fun.
@NoLlama But Albert Einstein didn't come up from nowhere, they knew before he was born that the theories were flawed under certain conditions, Albert Einstein "just" found how to solve some of the problems. In this case, the theory works perfectly well, therefore there is no place for an Einstein !
There was a man some time ago, who was saying : "We can't do science if we always test things we are sure about, we can't progress." And who was this guy ? Me, in this comment.
And so that's why we all have to thumb up ^^
Ah man, I love when my favorite channels do these crossovers.
Grant you have the sexiest voice I’ve ever heard!
YouTube Algorithm: You know what... people must be missing airplanes... Lets chuck a whole bunch of turbulence focused videos at em
3Blue1Brown - 2018-11-13
Thanks to those who caught my speako describing Kolmogorov as a "19th-century" mathematician. Of course, I meant the 1900's. His work is quite recent and remains relevant to a number of active research efforts in a surprising breadth of fields. It's crazy to me that his name is as relevant to fluid dynamicists as to those studying machine learning.
Jaskier - 2019-02-17
My calculus professor used to say "The shadow of Kolmogorov is large".
Atharva #breakthrough - 2019-05-30
Can you please do one on PCA- principle component analysis?
TETronski - 2019-10-14
Make the vortex stand in place. Sucking it backward or blowing it from the front, or both combined, could maybe do the trick.
TETronski - 2019-10-14
I see an analogy with the Lorentz force, visualizing this. Maybe wrong maybe not.
LowJack187 - 2019-10-26
Honk Kong: All your eyes are belong to Laser!