Let me spend 2 words to prize your incredible work. I am a PhD Student in boundary layer transition and I find all your videos incredibly interesting and high quality. Your videos are amazing and incredibly good in making complex things understandable. Keep going, your work is gold and may lead to a new way to promote science and scientific works.
In our company (casting pistons) , we are facing a problem of blow holes defect in the crown section. We are trying to resolve this using machine learning, and then field test these experimentally. Visosity might be contributing to the defect. But the problem is how to model this in ml project. Anyone having any idea?
It was really informative! Really enjoy your videos! I had a doubt, in the video at 27:11, when we evaluate the time averaged term, why aren't we dividing the integral by the total time i.e T in this case?
I was wondering the same thing! In Smits' lecture notes (linked to in the video description) p.203 he does divide by T. Indeed we have to divide by T otherwise Ubar diverges in the T->infty limit for any reasonable flow!
Great question! The wake usually refers to the fluid displaced behind an object moving through the fluid (like a truck or a boat). Turbulence is a particular type of unsteady multiscale fluid behavior with lots of scales of vortices interacting. So some wakes can be turbulent and other can be laminar.
Thank you very much for another excellent video! Love your content, the way you explain complicated stuff very intuitively and also the time you invest to teach us. I am just confused where the 1 over Reynolds term in your Navier Stokes equations comes from.. from my point of view, it should be the kinematic viscosity and 1/rho for the pressure gradient? I think when using the Reynolds number the units don’t fit in your equation. Or do you have dimensionless variables? In this case, we are missing a Reynolds number for the time derivates, don’t we?
@@Chipadychuck thanks for your answer. But when I am doing the non-dimensionalization, a Reynolds number remains in front of the time derivate. At least when I make the pressure and the time dimensionless with rho u^2 and nu/ u^2 to avoid the appearance of additional similarity numbers
From my Master of science in Iran at the University of Tehran in 2015-2018 all the way to now, I am following your channel and videos. I can see you are getting better and better every time in terms of quality, information, and so on. It may lead to a new way for education🤞 ❤! During my research (5 years) I always was trying to make a clear understanding of the concepts like: 1- Instabilities in fluid and 2-Transition from laminar to turbulence. It seems to be an interesting topic if you provide us a few great videos. Again, thank you, and keep up the good work!
The Reynolds decomposition feels like the first step in breaking down the flow in a hierarchy of scales, similar to a Fourier transform. The challenge is finding the basis of the scales where it would further simplify the analysis.
This looks really cool. I really enjoyed the qualitative introduction. For those of us w/o the engineering/physics chops (yet), this is a daunting subject, so thanks for that. Hat tip for the use of "zed" early on.
the work that you are doing is amazing. I am actually binge-watching your videos like it's Netflix. But I have a small request it would be amazing to make a whole course for fluid mechanics which dives deep into all the mathematics and underlying theorems. It is really amazing. Thank you very much.
Richardson (a major figure in aerodynamics) famously said...."Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity." Now that viscosity can be manifestly reduced by injecting ionized air into the flow field
@SteveBrunton, In [17.52], you mentioned the coherent structures of laminar and turbulent flow. However, I wonder why these wawe-like patterns are exist even in laminar flow, what causes these coherent structures. Let say we disturb the pipe in which fluid goes through at low velocities, can that be one of the reason wave-like pattern in laminar flow? Or I can ask the same question in this way : why these patterns exist in turbulent flow even if it's chaotic? I was confused.
In the name of Lord of the Universe the Most Merciful and the Most Compassionate Mr. Steve Brunton, I have found a small mistake (time snapshot of 27:50) regarding mathematical expressions of mean-flow, U_bar (x), you expressed that U_bar(x) = lim(T --> infinity) integral (from 0 --> T) of u(x,t)dt I think there is inconsistency in dimensionality, the RHS expresses the velocity multiplied by the increment of time whilst on the LHS the velocity itself. In order to avoid this dimensionality issues, it is better to insert " 1/T " outside the integral operation but inside the limit function to the RHS such that the dimensionality would be in equality for both (RHS and LHS), as represented below: U_bar(x) = lim(T --> infinity) (1/T) integral (from 0 --> T) of u(x,t)dt thank you,
how do we Determine the problem complexity for simulating turbulent flows around the wings and body of a supersonic aircraft. Assume that the number of grid points are around 10^(11)
4 dimensional. It exists within a timescale of causality. Any variation or derivation of, can alter the trajectory of a multi scale Multi point variable. To get accurate predictions you'd have to have multiple models running congruently, to monitor fluctuations or course corrections and cross compare. Right?
In many ways a well done video but one criticism that could be levelled is that in 30 minutes, you never get to substance. You skirt the issue in enthusiasm but is that good or wasting time. Maybe don't build up to a large series if it could be conveyed in 5 minutes.
Interesting question! I know that geophysical flows have enormous Reynolds numbers... astronomical flows must have Reynolds numbers that are... astronomical?
*Does Ryzen CPU and nividia GPU driver have issue ? I have heard from Tom Hardware website..... Can I run mechanical software like Openfoam, Hypermesh, Ansys(Simulation), Converge CFD, Ansa in ryzen smoothly and what about linux....can i go for hp omen (R5 4600H GTX 1650)*
My father Gleb Kerensky was world authority on turbulence in Hyrdro-Electric turbine pipleines and the dangers of water-hammer in them that could be destructive. In his late 70`s - early 80`s, he was consulted on the Snowy Mountain scheme in Australia, where he preformed a calculation that his colleagues told him would be impossible. I believe he had a patent on it, all the rest of his work was patented under the name of his employers, Engliish Electric/ GEC/ Alsthom. As these were cancelled out a a Japanese firm who made slight adjustments, he was suspicious of conferences and patents. You might find somethin helpful for the current debate.
On the turbulence, [10:08] and others, am I correct in thing that the turbulence itself is caused (and will occur in simulations) only because of random nature of the initial values for input values? For example, first two pictures (R
Hi, thank you very much for the videos, they are really good. Can you help me by giving me a path or a clue, about how can I calculate the length of a pipe should have in order to guarantee the mixture of 2 gases (natural gas and hydrogen). Suppose I inject H2 at a certain point in a natural gas pipeline, how can I know how far from that point I can guarantee a homogeneous mixture? I suspect that it is directly related to the Reynolds number, (gas velocity, diameter, viscosity, etc.) but I don't know how from then on I can know how far I guarantee the mixture. Can you help me by indicating where I should start?
Hi amazing video, from my understanding of viscous quantity is that if an atom's viscosity rate is high then it experiences less resistance past an object moving through fluid and the atom is gonna move faster thus less drag and vice versa, any feedback and correction would be appreciated.
An absolute pleasure to watch and understand the concepts lucidly. Your explaination is golden and I have become your fan. Thank you from the bottom of my heart.......
I'm new to this channel, in some of your lectures how do you write in such a way that you face us while writing comprehendible text? Are you writing backwards or is it some kind of editing where you write in the air and later add the notes to the video?
What a gorgeous video and the channel. Thank you a lot for a great, vivid and easy to get explanations. One thing could help a lot if this is connected to the real calculations. Math is abstract and difficult to catch sometimes, especially when it comes to fill the gap between the formula and real-life representation. If you accompany this with code which simulates the dynamics and show the mapping between formulas and code this could help a lot.
This is gold, also you are one of the few people that points out to really good papers and gives credit to everyone that motivates or gives you ideas... BRAVO!
If I have to study the whole turbulent dynamics to get the piece of information I need that is going to take a lifetime. Many people do that and just do nothing else. The most important is to connect the dots of every aspect of nature in one smooth flow of energy not wasting time.
Cus while you get confidence you got that right you missed 90% of the rest of the world around you. Yes you are perfect in 10% but you can not see the whole picture and you are already retiring.
"I don't really consider 2D flows as turbulence" * proceeds to show us a bunch of pictures of 2D turbulent flows * ;) (j/k, I'm absolutely delighted that you're going to present lectures on turbulence! Are you largely going to be following Smits lecture notes, or veering off into different areas?)
I know... I totally realized that half-way through the video :) For the first part, mainly following the Smits notes, but for the "modern deep learning" part, we will be looking at more contemporary literature.
Let me spend 2 words to prize your incredible work. I am a PhD Student in boundary layer transition and I find all your videos incredibly interesting and high quality. Your videos are amazing and incredibly good in making complex things understandable. Keep going, your work is gold and may lead to a new way to promote science and scientific works.
Thank you so much! Knowing that these videos are making a difference gives me all the motivation I need to keep making more!
Sending some ❤ from China
Thank for you for all the wonderful work you put into this video. Helped me understand the curiosities I am working on.
Truly Love your videos. I think apart from the four characteristics you mentioned, dissipation is another vital one.
Wow... what can I say! I am witnessing a top-tier scholar single-handedly making change happen to open science
Thank you so much -- glad you like it!
In our company (casting pistons) , we are facing a problem of blow holes defect in the crown section.
We are trying to resolve this using machine learning, and then field test these experimentally.
Visosity might be contributing to the defect.
But the problem is how to model this in ml project.
Anyone having any idea?
It was really informative! Really enjoy your videos!
I had a doubt, in the video at 27:11, when we evaluate the time averaged term, why aren't we dividing the integral by the total time i.e T in this case?
I was wondering the same thing! In Smits' lecture notes (linked to in the video description) p.203 he does divide by T. Indeed we have to divide by T otherwise Ubar diverges in the T->infty limit for any reasonable flow!
Yes, pretty sure that this is a mistake
Good call -- yes, definitely divide by T
Yes, should divide by T here
Yep
Great video! Thanks a lot. Going to see your other "lectures"
thank for sharing your knowledge. Is there any video on "unsteady reynolds averaged navier stokes equations" ( URANS )
Thank you steve
You are very welcome!
In an aircraft, What will be the effects turbulence magnitude between 1.5 to 2? Will it cause error in indicated airspeed?
Hokusai. Why was that artist not credited?
Apologies, I had an embarrassing blank on the name when I was talking through the slides.
Hello Steve, thanks for the videos, I have a very basic and maybe stupid question but what is the difference between turbulence and wake?
Great question! The wake usually refers to the fluid displaced behind an object moving through the fluid (like a truck or a boat). Turbulence is a particular type of unsteady multiscale fluid behavior with lots of scales of vortices interacting. So some wakes can be turbulent and other can be laminar.
Steve Brunton thank you very much for your quick and comprehensive reply. Thus how can we distinguish them from each other? By the fluid velocity?
Thank you very much for another excellent video! Love your content, the way you explain complicated stuff very intuitively and also the time you invest to teach us. I am just confused where the 1 over Reynolds term in your Navier Stokes equations comes from.. from my point of view, it should be the kinematic viscosity and 1/rho for the pressure gradient? I think when using the Reynolds number the units don’t fit in your equation. Or do you have dimensionless variables? In this case, we are missing a Reynolds number for the time derivates, don’t we?
These should be non dimensional units, including the time
@@Chipadychuck thanks for your answer. But when I am doing the non-dimensionalization, a Reynolds number remains in front of the time derivate. At least when I make the pressure and the time dimensionless with rho u^2 and nu/ u^2 to avoid the appearance of additional similarity numbers
Can anyone tell me what is the delta p value in the Navier-Stokes equation suppose to represent?
It’s actually gradient p and represents the gradient of the pressure in all spatial directions
@@estherpaulina6914 Thanks a bunch, appreciate it.
@@estherpaulina6914 Thanks!
It seem to me that such Navier-Stokes equation is wrong. To start it is not dimensionally consistent
?
You are single handedly upping my physics game
Awesome, love to hear it!
Not even Destin from Smarter Everyday disliked this video!
Why would he cause Derek already convinced him.
From my Master of science in Iran at the University of Tehran in 2015-2018 all the way to now, I am following your channel and videos.
I can see you are getting better and better every time in terms of quality, information, and so on.
It may lead to a new way for education🤞 ❤!
During my research (5 years) I always was trying to make a clear understanding of the concepts like:
1- Instabilities in fluid and
2-Transition from laminar to turbulence.
It seems to be an interesting topic if you provide us a few great videos.
Again, thank you, and keep up the good work!
Thanks so much for the kind words!
The Reynolds decomposition feels like the first step in breaking down the flow in a hierarchy of scales, similar to a Fourier transform. The challenge is finding the basis of the scales where it would further simplify the analysis.
This is exactly right!
This looks really cool. I really enjoyed the qualitative introduction. For those of us w/o the engineering/physics chops (yet), this is a daunting subject, so thanks for that. Hat tip for the use of "zed" early on.
the work that you are doing is amazing. I am actually binge-watching your videos like it's Netflix. But I have a small request it would be amazing to make a whole course for fluid mechanics which dives deep into all the mathematics and underlying theorems. It is really amazing. Thank you very much.
Richardson (a major figure in aerodynamics) famously said...."Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity."
Now that viscosity can be manifestly reduced by injecting ionized air into the flow field
@SteveBrunton, In [17.52], you mentioned the coherent structures of laminar and turbulent flow. However, I wonder why these wawe-like patterns are exist even in laminar flow, what causes these coherent structures. Let say we disturb the pipe in which fluid goes through at low velocities, can that be one of the reason wave-like pattern in laminar flow? Or I can ask the same question in this way : why these patterns exist in turbulent flow even if it's chaotic? I was confused.
In the name of Lord of the Universe the Most Merciful and the Most Compassionate
Mr. Steve Brunton, I have found a small mistake (time snapshot of 27:50) regarding mathematical expressions of mean-flow, U_bar (x),
you expressed that U_bar(x) = lim(T --> infinity) integral (from 0 --> T) of u(x,t)dt
I think there is inconsistency in dimensionality, the RHS expresses the velocity multiplied by the increment of time whilst on the LHS the velocity itself.
In order to avoid this dimensionality issues, it is better to insert " 1/T " outside the integral operation but inside the limit function to the RHS such that the dimensionality would be in equality for both (RHS and LHS), as represented below:
U_bar(x) = lim(T --> infinity) (1/T) integral (from 0 --> T) of u(x,t)dt
thank you,
Why though? Is laminar flow self-stabilizing somehow, preventing perturbations from growing? How?
how do we Determine the problem complexity for simulating turbulent flows around the wings and body of a supersonic aircraft. Assume that the number of grid points are around 10^(11)
4 dimensional. It exists within a timescale of causality. Any variation or derivation of, can alter the trajectory of a multi scale Multi point variable. To get accurate predictions you'd have to have multiple models running congruently, to monitor fluctuations or course corrections and cross compare. Right?
The mean flow equation seems like need to be multiplied by 1/T .
In many ways a well done video but one criticism that could be levelled is that in 30 minutes, you never get to substance. You skirt the issue in enthusiasm but is that good or wasting time. Maybe don't build up to a large series if it could be conveyed in 5 minutes.
Smits' notes are no longer (dec 23) available at the link in the description. Mind posting a copy at another?
Actually I do think one of the main factors people understand things hard
is slow talking
Don't let Destin hear you say this.
Underrated comment 😂
Thumbs up!!!
Thank you! Cheers!
Very nicely explained with wonderful slides and pictures. I can see how much effort had been put in these slides. Absolutely wonderful
Isn’t turbulence simply a real-world application of fractality?
I wonder what the Reynold’s number is for the surface of the sun.🤔
Interesting question! I know that geophysical flows have enormous Reynolds numbers... astronomical flows must have Reynolds numbers that are... astronomical?
@@Eigensteve ha makes total sense!
duh, it's so obvious, it's just that people who make low budget movies also love laminar flow
Might it be helpful to list links to the videos in the description in the same fashion the link to Lex Smits notes is provided ?
Thank You .
Love that. Your way of describing things is very inspiring for me. I hope this turbulence series will last long.
Glad you enjoy it!
Moore Edward Lewis Paul Martinez Helen
Someone said once that you don't understand the universe before you understand turbulence..
Turbulence? More like “Terrific video this is!” 👍
*Does Ryzen CPU and nividia GPU driver have issue ? I have heard from Tom Hardware website..... Can I run mechanical software like Openfoam, Hypermesh, Ansys(Simulation), Converge CFD, Ansa in ryzen smoothly and what about linux....can i go for hp omen (R5 4600H GTX 1650)*
It should work fine.
Does the flow have to be laminar everywhere in an ideal liquid?
Excited to which complete series on turbulence
Great introduction here! I love the examples, the simulations, and the connections to cinema.
Thanks so much!
That was lovely, keep up the good work!
Thank you very much!
I love your videos I am M. Sc. student in México and I really like your videos
Awesome! Thank you!
I must say that these lectures have always been fantastic, thanks
Glad you like them!
عالی بود. جریان در لوله ها یکی از موارد مورد علاقه من هست.
Excellent
Lovely content as always
Love from Reading, UK.
thanks steve
You are welcome!
Wonderful. Thanks for the lockdown education from Germany :) Keeping me sane.
Great to hear!
awesome video you kilt this!
Anyone else struggling to download the notes?
Thanks! Really helps for an analysis of Vertical Savonius wind turbines im working on!
Glad it helped!
looks like he floating in the air
Just a floating head and arms...
@@Eigensteve yh
Great vedio, thanks :)
Glad you liked it!
Absolutely love this. Quick question, is the link to Prof. Smits lecture notes down?
I just checked the link and it is working for me.
My father Gleb Kerensky was world authority on turbulence in Hyrdro-Electric turbine pipleines and the dangers of water-hammer in them that could be destructive. In his late 70`s - early 80`s, he was consulted on the Snowy Mountain scheme in Australia, where he preformed a calculation that his colleagues told him would be impossible. I believe he had a patent on it, all the rest of his work was patented under the name of his employers, Engliish Electric/ GEC/ Alsthom. As these were cancelled out a a Japanese firm who made slight adjustments, he was suspicious of conferences and patents. You might find somethin helpful for the current debate.
So many amazing examples, love it!
So glad!
On the turbulence, [10:08] and others, am I correct in thing that the turbulence itself is caused (and will occur in simulations) only because of random nature of the initial values for input values? For example, first two pictures (R
Nice and good course, go ahead, it will be very interesting.
Yes, thanks
thankyou ....nice explanation of concepts. :)
P.s : plz make a video also on various length and time scales in turbulent flow
Hi, thank you very much for the videos, they are really good.
Can you help me by giving me a path or a clue, about how can I calculate the length of a pipe should have in order to guarantee the mixture of 2 gases (natural gas and hydrogen).
Suppose I inject H2 at a certain point in a natural gas pipeline, how can I know how far from that point I can guarantee a homogeneous mixture?
I suspect that it is directly related to the Reynolds number, (gas velocity, diameter, viscosity, etc.) but I don't know how from then on I can know how far I guarantee the mixture. Can you help me by indicating where I should start?
Loved this video!
Hi amazing video, from my understanding of viscous quantity is that if an atom's viscosity rate is high then it experiences less resistance past an object moving through fluid and the atom is gonna move faster thus less drag and vice versa, any feedback and correction would be appreciated.
Very cool thx
Speed x2
I hope you and your family are doing well. I would like to say the explanation of this video was wonderful. Thank so much you Sir.
I just LOVE IT!! I really can not describe how content I am just watching this video. Keep up the good work (y)
An absolute pleasure to watch and understand the concepts lucidly. Your explaination is golden and I have become your fan. Thank you from the bottom of my heart.......
I'm a geology major and i needed to learn about this to study sedimentology and it was so helpful!! thank you!!
👏👏👏
Fascinating!
🌀
Great video as always, the ease you explain these things
Glad you like them!
I'm new to this channel, in some of your lectures how do you write in such a way that you face us while writing comprehendible text? Are you writing backwards or is it some kind of editing where you write in the air and later add the notes to the video?
Beautiful lecture thank you! Found a free pdf of ‘an album of fluid motion’ incredible, thank you for sharing.
Thank you for this excellent video
You are very welcome
What a gorgeous video and the channel. Thank you a lot for a great, vivid and easy to get explanations.
One thing could help a lot if this is connected to the real calculations. Math is abstract and difficult to catch sometimes, especially when it comes to fill the gap between the formula and real-life representation. If you accompany this with code which simulates the dynamics and show the mapping between formulas and code this could help a lot.
Absolutely beautiful. Thank you, Steve. I hope the good you put into the universe comes back to you ten fold.
It's outstanding this content is free! This is one of the best explanation about turbulence I've been explained
Well done
Thanks!
Love your videos Dr., are you planning to make a video about coherent structures?
This is gold, also you are one of the few people that points out to really good papers and gives credit to everyone that motivates or gives you ideas... BRAVO!
should there be a 1/T in the Ubar(x) equation?
Excellent summary !
Glad it helped!
This is such a well-organized intelligible lecture. Thank you for spending the effort and time to make these lectures public for us!
Love your work! Amazing lecture!
Great content Steve I’m really enjoying this series!
Thanks for your incredible work!
If I have to study the whole turbulent dynamics to get the piece of information I need that is going to take a lifetime. Many people do that and just do nothing else. The most important is to connect the dots of every aspect of nature in one smooth flow of energy not wasting time.
Cus while you get confidence you got that right you missed 90% of the rest of the world around you. Yes you are perfect in 10% but you can not see the whole picture and you are already retiring.
Great! you are an excellent teacher
This is going to be the best series yet, I can't wait a whole week between instalments!!
Me neither :)
"I don't really consider 2D flows as turbulence"
* proceeds to show us a bunch of pictures of 2D turbulent flows * ;)
(j/k, I'm absolutely delighted that you're going to present lectures on turbulence! Are you largely going to be following Smits lecture notes, or veering off into different areas?)
I know... I totally realized that half-way through the video :) For the first part, mainly following the Smits notes, but for the "modern deep learning" part, we will be looking at more contemporary literature.
@@Eigensteve Awesome. I've been slow to get on the deep learning hype train, but it looks like this will be a perfect way to ease myself on board ;)
I love turbulence. I don't fully understand it. Nobody fully understands it. That's what I love about it. :-)
Me too!
I've always loved how complicated turbulence is. Structure and chaos.
Agreed. Very fascinating.