The ultimate fluid mechanics tier list

Fluids can do really cool things, but which things are the coolest? Soon-to-be-Dr Kat from the University of Bath, studying for a PhD in fluid mechanics, put fluid effects including laminar flow, vortex streets, and the Kaye effect.
What's this based on? Almost entirely just vibes.
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Music by Epidemic Sound: epidemicsound.com
Some stock footage courtesy of Getty.
Edited by Luke Negus.
This guest video from KatDoesMaths on Twitch is about fluid mechanics, which fluid effect is coolest, and ranking fluid mechanics in a tier list. Kat talks about phenomena including vortex sheets, bouncing droplets, viscosity, turbulence, and laminar flow. If you like videos from Stand Up Maths, 3blue1brown, Flammable Maths, Andrew Dotson, Numberphile, and Steve Mould, you'll like this fun video about maths and a tier list of fluid dynamics.
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[@ThomasRintoul]

Loved this! Though I'm not sure I can forgive putting the Rayleigh-Taylor instability in D tier. Turbulent flow is cool!!! We don't need analytical solutions!!!

[@JCisHere778]

There are a few analytical results and "solutions" for turbulent flows :) .

[@mastershooter64]

@@JCisHere778 woah really??? can you give some examples?

[@JCisHere778]

@@mastershooter64 There are some results like the Betchkov (I hope that was the name :) ) invariants that are disconnected from the Navier-Stokes equations and others like the law-of-the wall (and many other turbulent scaling laws) which can be rigorously derived through symmetry analysis of the governing equations. However, the latter should be taken with a grain of salt as they are more of a prototypical solution than an actual solution.

[@abyssaljam441]

An Analytical solution would make designing fluid systems so much easier though. You wouldn't have to spend weeks doing a CFD runs or tunnel tests to work out the best configuration of a thing. Just Excel and goal seek.

[@harris8462]

@@abyssaljam441 Hi! Highschooler here, trying to make a CFD of a Pulsating Heat Pipe. Any resources I could use to learn how to build a CFD model?

[@juanfelipecespedes6704]

You would think that a mathematician would put turbulence, the most important unsolved problem in classical physics, up in the tier list due to the challenge of its complexity. #MillenniumProblem

[@vigilantcosmicpenguin8721]

Perhaps it's simply fear of the unknown.

[@user-oe2uq1mi9t]

@@vigilantcosmicpenguin8721 yeah, im scared to look at my asshole

[@jhawar-ji]

Laminar Flow in C tier! I have seen everything in my life. My will to live has left my body.

[@kaudsiz]

🤘☹️🖤🌈

[@aminsabir7902]

Destin from Smarter Everyday, leaves the room in rage 🥲

[@professorfrog7181]

L*minar flow 🤮

[@nikospud860]

Amazing stuff. For the first time I am convinced that Kat is a mathematician and not a physicist based on these rankings. #Justice4Laminar

[@KatDoesMaths]

It was the only way to convince people

[@dougdimmedome5552]

But she ranked smoke and even bubble rings so low, not forgivable.

[@professorfrog7181]

L*minar flow 🤮 is cringe and it deserves F tier the only justice for it would be getting put in the trash bin where it belongs. Turbulent flow is S tier.

[@MrSam2450]

I’m happy there was no Fog fiasco in this great tier list. Fog is S tier

[@ThomasRintoul]

I dunno, from the comments it would appear that Turbulence Gang is rising

[@professorfrog7181]

The turbulence fiasco is orders of magnitude worse. L*minar flow ranked higher I feel literally physically sick I can't.

[@juanmairal7048]

Mostly agree but I can't allow Turbulent Flows to be left in the F tier. A problem that scared both Feynman and Heisenberg deserves a much higher position imo. Seriously, as a PhD student of CFD myself I loved the video and I appreciate how a tough topic like fluid dynamics is made very approachable. This is some top tier science communication and I am definately returning to this for inspiration for my next talk.

[@charliemw333]

As a CFD engineer I see no problem with turbulence, it's easy to work with, just slap a RANS model on top and pretend it's another passive scalar. Turbulence is clearly S tear 😢

[@fg8557]

Approximating the effect of the turbulence shear stress tensor by one or two scalars 💀💀

[@saifmukadam5261]

Hey I wanted to start studying CFD I wanna know what topic pick up on like research paper and stuff

[@ibonitog]

I will never forgive you for your Turbulence-F-tier choice!! :D chaotic systems and the mathematical process of (seemingly) random behaviour arising simply from the non-linearity of deterministic systems is so deeply fascinating and beautiful to me!

[@p_mouse8676]

The thing with laminar flows is not about its simplicity, but how rare pure natural laminar flows are. They barely exist. One tiny bump can ruin your perfect flow completely, some taking the whole thing to the other extreme.

[@icskatingqn]

That was really cool, thanks for sharing Kat, and for elevating her work, Simon!

[@TheOllieJackson]

As someone currently doing their PhD in Vortex Ring dynamics... I think they're neat

[@Respectable_Username]

I love how vibes based the actual rankings are alongside being shown super cool phenomena. Great video! ❤

[@dungeonseeker3087]

Here's an interesting one, in Chemistry there's a thing called the Briggs-Rauscher oscillating reaction, not only does it look kinda gorgeous but I have to imagine there's some funky stuff happening inside the reaction material too.

[@TheMorris360]

I disagreed with almost every pick, but I still loved this video. Great work!

[@Nartinan]

Fire is arguably another multi-layered fluid phenomenon. Combining interesting fluid dynamics with chemical reactions, phase changes and (somewhat limited) self-sustainability. Considering its beauty and utility, but also the relentless chaos and violence is causes, it's an easy S Tier for me. Also, I can't believe you put the Crabby Nebula in D Tier.

[@mikefochtman7164]

Nice stuff. I remember learning about 'Taylor bubbles' when we were studying boiling water in power plants. The vapor formed when boiling water has to travel up the tubes inside where it was heated. Small bubbles with a large amount of liquid flowing wasn't a problem. But as you add more and more heat, the bubbles coalesce and eventually 'fill' most of the tube. Now you have a wholly different flow behavior that impacts the heat transfer with the tube wall. Fluid flows are so wonderfully complex, even for something as 'simple' as water. :)

[@JCisHere778]

I find turbulence especially beautiful from a mathematical perspective. Especially the fact that the phenomenon is governed by a linear functional equation always baffles me... Also, there are a few really nice analytical results for turbulent flows that are rather surprising

[@olivier8223]

how are the equations linear? the NS-equations are nonlinear

[@JCisHere778]

@@olivier8223 They are, but the evolution of a statistical ensemble is governed by the Navier-Hopf functional differential equation. This is derived from the Navier-Stokes equations but is indeed linear :). P.S. you kinda exchange non-linearity for infinite dimension. So it doesn't do you much good

[@adolfobahamonde2358]

​@@JCisHere778 But also shouldn't dissipation impose a cutoff and the effective dimension of the attractor generated by the dynamics should be finite but super high-dimensional? Like a finite dimensional structure embedded in an infinite-dimensional space 🤯

[@pablo_CFO]

I almost die when I saw "Turbulent flow" ranked in the F tier and "Vortex rings" in the E tier... and i understand that this ranking was based on different types of fluid flows rather than specific techniques. However, for me, Lagrangian Coherent Structures represent the most beautiful way of visualizing fluid flows. ❤

[@vblaas246]

Suggestion: Some planetary flows could be included, like coriolis effect, saturns hexagon and jupyters towering cloud bands? Awesome video. Rayleigh instability in a water tap should be higher tier for being so commonly overlooked.

[@yoavshati]

0:08 no way! I'm not the author of Firmament: The Hidden Science of Weather, Climate Change and the Air That Surrounds Us too!

[@vigilantcosmicpenguin8721]

I'm not saying I'm the author of Firmament: The Hidden Science of Weather, Climate Change, and the Air that Surrounds Us, but nobody has seen me and the author of Firmament: The Hidden Science of Weather, Climate Change, and the Air that Surrounds Us in the same room.

[@mudgetheexpendable]

Not that it matters, but I completely agree with your higher placement of the ring bubble on grounds of coolth. Fun video, thank you and Simon for it.

[@user-xsn5ozskwg]

I adore living in an age where I get to see scientists and mathematicians share their interests and studies in such an accessible and fun way. I can't help but feel the call to explore each example in depth and find out even more. I won't stand for the train slander though.

[@lad4694]

If you've ever seen some weird spirals around some long smoke stack, tower or chimney (or those old car antennas), they're to mitigate the effects of the Von Karman Vortex sheets. I came across it after googling something F1 related and now can't stop seeing it everywhere on my way to work

[@bruceelder208]

I refuse to accept that laminar flow is C tier. There is no other type of flow that I get more hyped for than when I read the words "assume Laminar flow".

[@dubious_potat4587]

3:17 Destin is not gonna be happy about that

[@lazaraza]

Turbulent flow in the F tier?!.. ...but hey, it's your video.

[@declansalisbury5698]

as an engineer student we need turbulent flows, but I see why a mathematician doesn't like it, as the models are very hard to do via computation, we usually use wind tunnel data to analysis turbulent flows.

[@professorfrog7181]

No no, don't bunch mathematicians together with miscreants, plenty of mathematicians are appreciators of turbulent flows like everyone should be. It is a millenium problem after all.

[@neonbricks8182]

I did my final project in undergrad on bouncing droplets/walking droplets and took long(and 3 vibration generators breaking) to actually get the set up work and still have questions about the results we achieve, very frustrating but also very fun once set up correctly.

[@baksatibi]

Kelvin-Helmholtz instability can also occur in the air, creating beautiful repeating wave-shaped clouds.

[@lilcrowlet1802]

bro I'm just hydrology student, that's too many fluids that aren't water

[@dougdimmedome5552]

It’s a crime for a mathematically oriented fluid mechanics person to put smoke rings in E tier.

[@trevinbeattie4888]

I can see how the rankings would change a lot depending on whether you are looking at just modeling the behavior or only at its aesthetics.

[@Thoran666]

My favorite part of the morning: Study the fluid interaction of hot coffee and cold milk as well as the chemical effects of the fluids on the human nervous system.

[@moydodir79]

Great idea, but as aerospace eng, must absolutely disagree on the rankings 🤣🤣🤣. Supersonic flow, turbulence, Von Karman, RT instability, vortex rings - all should be at least C, and more likely B and above 🤣🤣🤣 Thanks for the reminder of how cool is fluid dynamics :)

[@ThePrimevalVoid]

NGL, I didn't know what I was going to see when I clicked on this video, but I enjoyed it a lot!

[@anindyaguria6615]

You could have added plasma and MHD as well. They are pretty neat😂

[@ma5t]

Really enjoyed this, although I disagreed with a lot of the placements! To me, it's the difficulty and chaos of turbulence that makes it so beautiful.

[@IndustrialBonecraft]

"There was a story about the quantum theorist Werner Heisenberg, on his deathbed, declaring that he will have two questions for God: why relativity, and why turbulence. Heisenberg says, “I really think He may have an answer to the first question." - James Gleick, Chaos

[@hansolo9892]

Yeah, it's a real shame how it got the lowest ranking here.

[@IndustrialBonecraft]

@@hansolo9892 For real, though, I understand the low ranking. Not as a 'this is awful' but more just the collective frustration of a million scientists going "Are you fucking serious!?"

[@hansolo9892]

@@IndustrialBonecraft haha agreed

[@CarFreeSegnitz]

9:47 That’s a vapour cone not a sonic boom. Vapour cones are caused by water vapour traversing a rapid pressure change. The air in front of the aircraft is compressed and able to hold on to more gaseous water. There’s a rapid transition to low pressure along the body of the aircraft which has less capacity for gaseous water so the water transitions to visible droplets. Very quickly behind the aircraft air pressure returns to normal and the visible droplets return to invisible gaseous water. Sonic booms are seen briefly during rocket launches between the cloud layer and space. It’s the layer that’s too thin to hold much water vapour but still thick enough to host sound waves. Not as much footage out there and not as impressive as vapour cones.

[@trs5127]

Laminar flow deserves S tier just for how satisfying it is.

[@theresalwayssomethingtobui944]

Cool idea! Yet, as an environmental engineer, I would order this completely different! Turbulent flow is amazing for the environment, otherwise e.g. water bodies would die due to Oxygen loss! A tier! And Taylor Instabilities are so cool too - at least C tier!

[@likebot.]

"... turbulence is often where a lot of our _current_ models will break down". Why did I find that funny?

[@gasdive]

When you mentioned dense above, less dense below, I thought i was going to see Rayleigh-Bénard cells. Was also hoping for some Bose-Einstein condensate.

[@spencerthomas4087]

A lot of these lower tier entries remind me of subjects in my field where I tell my colleagues "that's really cool or would be very useful - I really hope someone else gets on that"

[@pavel9652]

I didn't realize there is a specific fluid dynamic effect in play in the planetary nebula.

[@jamesbobrob]

How about some love for the Richtmyer-Meshkov instability, or what you get if you combine a supersonic shock with a Rayleigh-Taylor like density difference

[@datguy6101]

Great video!

[@kendrajohnson6535]

Very, very cool! Loved the ferrofluids :)

[@kayleejade7227]

this is literally my favorite video on all KZbin

[@melissamybubbles6139]

The bouncing water droplets are pretty neat. Thank you and Simon.

[@abyssaljam441]

Can a perfect fluid, like those used in potential flow calculations, be compressible? I asked my lecturer last week and he didn't know of the top of his head.

[@BraneTheory]

Turbulent Flow in F tier painful 😂

[@jonathandevries2828]

"TURBULANT FLOW IS BETTER!!" -Some guy outside of Destin's house probably...

[@xaviergonzalez5828]

Nice video Kat, I'm looking for information about fluid dynamics masters degree programs. This video it's really handy for me! Thank you!

[@mh1593]

Good call on the Pi ear rings!

[@benmcreynolds8581]

I love Turbulent flow. Its the most facinating thing

[@PolygonAlley]

That Brainiac clip has lived in my head rent free for 15 years.

[@zeldovich33]

Oh I notice that combustion, plasma and nuclear is missing, I work with Ritchmyer meshkov instability whit shock flame interactions. Also detonation phenomena. A lot of perturbation methods, pde and so many cool things

[@benmcreynolds8581]

Could cavitation bubble's be a part of this?

[@benmcreynolds8581]

What about the way they make Kodak film? Like layers of different laminar flows of different fluids to make multilayered film?

[@AttackSpeed407]

Considering plasma is basically a superheated ionized gas, does that mean it has its own unique fluid mechanics? Or is it something different altogether?

[@pavel9652]

Bouncing droplets are overrated. In Ireland rain bounces of everything and even rains sideways. It is called lashing rain ;) July 2023 was the wettest July on record and it was a complete nightmare.

[@mastershooter64]

Now do the ultimate magnetohydrodynamics tier list

[@EladLerner]

Laminar Flow C tier? *Destin has entered the chat*

[@lyrimetacurl0]

I thought it would be CFD models tier list (like k-epsilon, BSL Reynolds Stress etc).

[@ThePrimevalVoid]

9:45 Wait, do we not already consider air to be a compressible fluid? I feel like otherwise a lot of early thermodynamics doesn't make much sense.

[@JCisHere778]

There is no such thing as an incompressible fluid. However, different flow phenomena can be treated as either compressible or incompressible, governed by the Mach number, Helmholtz number, etc..

[@KatDoesMaths]

In practical terms yes It's compressible, however when you're in 'low speed' regimes, we often treat it as incompressible to make the systems nicer. It's one of those assumptions that if you wanted to include every single fact about the fluids you'd put it in, but the difference in effects is so small it's not needed at the lower speeds and makes the maths simpler.

[@jaylentracey1051]

Air is much happier to just move out of the way rather than compress- think like when you open a door. So you just treat is as incompressible for systems working under the speed of sound

[@Finnspin_unicycles]

@@jaylentracey1051 well, incompressible under mach 0.3 is the general rule of thumb, above that it depends on the exact problem.

[@jen_sen8508]

The fluid dynamics of dihareah severity

[@Refract3d]

@SmarterEveryDay would probably disagree with your placement of Laminar flow!

[@jessicatymczak5852]

I have written code to solve the Navier-Stokes equations, and talk about pathological. Energy dissipation in turbulent flow is not well done.

[@mikkelkragh1336]

Bonus points for referencing Ghost In The Shell

[@Dragrath1]

Dismissing turbulence as F tier because it involves non analytical solutions automatically is a red flag for a scientist after all in the absence of friction or another comparable constraining force all fluid flow or any other 3+ dimensional system of partial differential equations are turbulent and or otherwise nonlinear and chaotic. We have a strong bias against nonlinear mathematics which is probably a consequence of our brains not having evolved to handle such things but that says more about us than the universe. Again chaos is the norm not the exception, dismiss turbulence and good luck finding away to not violate conservation laws.

[@hansolo9892]

"Chaos is the dark side of nature that we aren't ready for yet."- I remember my non-linear dynamics professor saying this quote once.

[@otsokivivuori7726]

Destin from Smarter Every Day would be horrified with your placing of laminar flow

[@khernrhun8220]

Some part I known, some I don't. Some I didn't understand but the fact tht KETCHUP is nonnewtonian will stay with me forever :D

[@rorrt]

What did laminar flow ever do to you?

[@caaaick]

What do you think about Saffman Taylor's problem?

[@KatDoesMaths]

A tier, we love a thin film

[@johnmartinez2445]

Laminar flow…. IN C TIER!!!! I’m dying. Laminar flow is my baby as a process engineer :(. We gotta get a better ranking for the king of applied fluids, laminar flow!!

[@AakeTraak]

This must be the best of the Simon Clarks...

[@erineosto]

So cool!

[@brucewinningham4959]

THANK YOU for posting this Informative & Interesting Video, Beautiful Lady.

[@kilmermad3306]

When you say draw a wave and my brain goes to a sine curve 😂

[@VoidHugger]

This video is just "how many other science KZbinr's videos can we use in a single video"

[@vigilantcosmicpenguin8721]

First, Simon put cirrus clouds in D-tier. And now you rank laminar flow as C-tier, to the chagrin of Destin-heads everywhere? This channel's tier lists really have a way of rocking the boat.

[@tadhgtwo]

Now that's a ranking video. No space give to fog.😂

[@angustin6590]

Nice

[@simtill]

Cool!

[@mitchhowe2201]

Excuse me! Complex fluids are way more than just shear thickening/thinning - they are any fluid composed of more than one state of matter. The stress-strain moduli can be so unpredictable in their behavior that there isn't even a classification, one simply just has to plot the data. There are also fascinating behaviors like viscoelasticity that are accurate models for so many industrial, environmental, and biological materials and are still not well understood at all. I think complex fluids are pretty cool. Sincerely, a graduate student studying complex fluids.

[@pitsielias483]

You can't put turbulence 😢 at trash tier 😢 its unforgettable 😂😂. Like the fact that it breaks most of mathematics 😊what a beauty

[@grg7452]

UPSTREAM CONTAMINATION!!!

[@JohnVKaravitis]

What language is this?

[@Henrik26]

I see my ketchup with a completely different set of eyes now.😂

[@carlospenalver8721]

I knew superfluity, like would it happen on earth if gravity reached minimum newton and cause what looks like the great flood in that once upon a time famous book people still read where the water rising up everything palm trees, houses, mountains, planes, trains and automobiles even if just 1mm thin would have everyone say the whole planets flooded without the need to add water to earths already existing volume explaining where the heck the water went. Yep U 4 Got SuperDooperFluidus. Cue in the star wars theme.

[@Chris-io2cs]

great video! but I do have to say that mixing in background music without a really good mic is.. a bit difficult on the ears, especially during the intro

[@TheCosmicGuy0111]

Woah

[@adnankassem8114]

Fantastic video! But some of those ranking decisions were blasphemous at best and an outright criminal offence in other cases. But I did enjoy the video!!!

[@tonywilson4713]

Aerospace engineer here and I hate to break your Sheldon Cooper math bubble but all aerodynamics involves compressible fluids NOT just supersonic flight because air is (that's right) compressible. Its not that compressibility effects magically go away they are simply less significant at lower speeds. Just remember you maths geeks come up with formulas while us engineers learn how to use them. 🤷‍♂🤷‍♂ And before you complain just remember the next time you're in a jet at 35,000ft doing Mach 0.8 it was a smartass like me who designed the wings that are keeping you from falling from the sky. P.S. I did like the video. 👍👍

[@professorfrog7181]

Imagine considering compressibility effects at M < 0.3 💀 Also you win most cringe comment of the year for your opinion of math

[@tonywilson4713]

​@@professorfrog7181 Since you want to be a smart ass. I actually studied aerodynamics AND PASSED so I kind of know this stuff and am fully aware what terms we drop out of the Nav-Stokes at various conditions. Which is something you clearly don't get. So if I get a cringe award from the math geeks WTF do you clowns get? I know - how about the computer your in front of right now or the electricity that powers it. My kind just makes it possible for M0R0NS to travel safely at 35,000ft rather than trying to figure out how droplets of water land in a puddle. That's the difference between math-geeks and engineers - WE MAKE STUFF WORK!

[@Alfa-FSB-Agent]

Cant even believe you put tủbolance in F tier

[@trulybengali]

Turbulence in F tier because your assumptions break down !! Nonetheless, a good four-minute video.

[@wallacetf]

I'm a laminar flow guy

[@RaglansElectricBaboon]

I like your make up more than Simon's. Also I'm trying to place your accent.. South Wales but not at all strong? Can you tell I didn't enjoy the terrible maths lecturers our Engineering department had?

[@KC_G4S]

Laminar flow is S Tier 🤬🤬

[@professorfrog7181]

I will literally fight you over that ungodly opinion that's where turbulent flows belong, l*minar flow is F- Sword or duelling pistol, you have the right to choose