Turbulence Closure Models: Reynolds Averaged Navier Stokes (RANS) & Large Eddy Simulations (LES) 

I think it's great that this video can be cited with a DOI. Videos like this represent genuine science and knowledge, communicated in a practical and efficient manner.

Arguably the clearest explanation you”ll find of the Reynolds stress closure problem. Beautiful.

Hi Prof, just to let you know. You've encouraged me to return to university for an MSc in Computational Science after some years in industry as a Process Engineer. Thank you for this making this material easily accessible.

Kudos for the great work! This is turbulence modelling made simple.

Prf Steve explain all the turbulence in just 30 min video. I am really excited to the next video on this lecture series.

Explained everything in very detail in such a short time.Incredible!!

What a passionate and clear explanation. Thank you Steve

Great work! You explain all the complexity of turbulence modeling in a very simple and elegant way! I'm looking forward to the next video!

Thanks for opening up these closure models. Keep posting !!!

Some people binge watch Netflix. I binge watch Steve Brunton's RU-vid channel.

I have a final in my turbulence modeling class tomorrow, so the timing of this video is impeccable. Thank you!

specifically amazing and well-prepared slides and more the point, informative.

Outstanding, instant subscriber. A rigorous and wonderfully lucid presentation that was easy to follow for a biophysicist who formally studied fluid mechanics forty years ago but listened to a father that specialized in turbulence who came out of John Lumley's era at Penn State in the 1960's. Really like how you overlay the equations and appreciate the attention to detail.

this series is amazing! I am a soooooo inspired by those lecturers

Hi Prof, you did an excellent job here and I am happy I have access to this video. It will help a lot in my research methodology. I am currently doing my Msc research on backward facing step flow and this will be amazingly useful. I have also downloaded the Lex Smith's lecture you referenced. Thanks once again for putting out this great work. Casimir Agbakaja

It was extremely beneficial for me to reorganize my thoughts in this field. Thanks

Really impressed sir. love from U.P., India. waiting for your next video of this series.

How lucky to be at that time to be able to see this class. Thank you

thanks for the lecture! Keep up with these videos!

i was desperately looking for such clear explanation(: amazing. Thanku professor

Great lecture! Thank you for sharing.

Thank you so much! This helped a bunch in understanding this topic!

Very nice discussion. It is true that Smagorinsky became head of the GFDL laboratory, but the development of LES occurred much earlier when he was a student of Charney and von Neumann. His early simulations of atmospheric flow showed some unphysical oscillations. von Neumann suggested he use the "artificial viscosity" that Richtmyer and von Neumann had developed to control unphysical oscillations in flows with shocks. Smagorinsky wrote a very nice paper about the origin of LES. Both shocks and turbulence are examples of high Reynolds number flows.

Very useful info. Especially @28:09, where Reynold's number definition is given in a much more clear and concise manner, relating eddy sizes!

You explain this waaaaaayyyy better then my professor at UCF.

Fantastic job! Nothing more to add.

Thanks for the great lecture!

Steve you inspire me!!!! I want to be like you and know as much as you do!!!!

Steve, well explained!!!!

C'est très beau, c'est très esthétique, c'est très français dans la manière de présenter la science telle des tableaux, comme suspendus dans l'air. Le savoir s'incarnant merveilleusement dans toutes ces équations et graphiques bariolés de mille couleurs chatoyantes.

Amazing course, thank you so much.

I think an error can be found at around 4:40, because to average U, you need to divide the integral from 0 to T by T, congrats for that great video! :)

Steve you are the 🐐 Feynman would love this

I wish I had a prof like him

Love this video so much!

Beautiful lecture

Great work! Thank you for the excellente explanation. :)

Very useful Sir, thank you very much!

👏👏👏 Wish I had this when I was doing my PhD.

Great lecture! Minor thing but I think you may be missing a 1/T in the mean flow equation @4:14

Wonderful. You have helped me

Thank you for the excellent lecture! I wrote an entire CFD software bassd on lattice Boltzmann (on my GitHub), and there you try to resolve all scales directly in the grid with gigantic resolution. However GPU memory sets a limit on resolution. If the Reynolds number becomes too large and resolution is not high enough, the simulation becomes unstable. Smagorinsky-Lilly LES provides a nice solution in ~12 lines of code: another way to think about LES is that you increase viscosity where shear rate is largest. Coincidentally, these are the very locations where instabilities would first occur. So LES makes the simulation nice and stable at large Re. I have some demos on my YT channel where I simulate entire airplanes with this.

Very nice explanation. :-)

I think an error can be found at around 21:50, there is no rho since it's Kinematic Eddy Viscosity, congrats for that great video! :)

Wow... Great sir...

I like Very much the interfacial sublayer, very very close with the surface

Superb 👍

Not only k-€, but virtually all eddy viscosity models over predict the production of kinetic energy. It is an inherent shortcoming caused by the eddy viscosity assumption itself. Too much kinetic energy leads to excessive viscocity, which means greater mixing, which again means greater ability to withstand adverse pressure gradient.

Good review material! As an experimentalist, I've been thinking about this for a while. I have three questions that I would appreciate your thoughts on: (1) Is it reasonable to use the wall distance as a distance for the closure equation? This sounds reasonable to me within the developing boundary layer, but not in the wake of a bluff body, for example. Or is the argument something more along the lines of "this is the best option we have"? (2) If I'm understanding 19:34 correctly, the turbulent viscosity is proportional to the distance from the wall squared? Is that the case generally for RANS turbulence models? I found in my experience that CFD models seem to over-diffuse regions of vorticity in the wake of lifting bodies (say, the vortex pair by a wing) when compared to experiments with exactly matching conditions. It looks to me that the fundamental issue then would be the incorrect choice of the length scale, then? i.e., if a proper vortex is formed in a wake, the length scale is no longer order wingspan, but order vortex diameter; (3) This type of turbulence modeling seems to implicitly assume the spectrum of turbulence as a generic turbulence cascade. If there's feedback behavior, a RANS model should be incapable of generating good predictions, am I correct? What about instabilities? In any case, thank you so much, Prof. Brunton, for laying this out so clearly!

Lift is caused by compression to the bottom surface of the wing and the top accelerating the downwash if you look at the top like a key slot and the bottom like a skipping rock.

Great explanation. But i have doubt over what time T this averaging is done?

THAT INTRO WOW

Actually Reynolds averaging is not REALLY time averaging, but statistical averaging ;-) which comes quite close but mathematically different. And RANS modelling does not necesserally comes with "simpler equations to solve". The trick is to solve RANS equations on much much less cells than you would do with DNS. Nice video anyway !

Great lecture Prof. Brunton. Just one query, in 18:50 shouldn't it be the Kronecker delta function, instead of the Dirac-delta function? And one small typo: 1/T term missing in the definition of the mean flow at 04:12.

Do you have a video with an explanation of the physical meaning / relative importance of the different terms of the Reynolds stresses ? Like, how is the magnitude of the pressure term -2/3 rho. k compared to 2.mut.dU/dz, and also their respective signs ? Thanks a lot, great lecture.

Do you have any video explaining k-epsilon and k-w models in more detail? Thanks for this video was so useful.

Superb lecture yet I am wondering if you haven't missed a 1/T in the mean flow calculation?

There are several gaps in the presentation that would confuse any beginner significantly. For example, the jump from the Reynolds stresses equations into the kinetic energy equation before introducing the eddy viscosity assumption, which is the main reason why the people started thinking about the kinetic energy.

It's Just great .

Feel like I'm watching Netflix episodes. Thank you!

Great lesson thank you. But, wasn't it Richardson the one who formulated the energy cascade theory? Kolmogorov is just the smallest scale, where energy dissipates due to viscosity, if I remember well

Can you please explain the concept of unsteady RANS? It would make sense to use RANS over steady state simulations because you need to take time average for a certain amount of time.

In x-momentum equations, left side is a scalar and right is a vector....

Hi Steve, what’s the difference of nu_t for a 1 equation model and a 2 equation model? I guess in the first case we imposed nu_t being uniform during all the time calculation whereas in the second case we calculate nu_t based on k and epsilon equation and it changes during the calculation time

For LES, Isn't there a video for the deduction of LES equation from N-S eqs as you did for RANS? Thank you.

When it comes to physics, what is the difference between diffusion and dissipation?

Very informative, but I have to note this @18:50 you say dirac delta function, but is not. It's the Kronecker delta function, since we are dealing with equations with Einstein notation.

k-w however is much better for adverse pressure gradient, isn't it? I always thought that to predict local flow detachment in small scales that was the way to go! Am I wrong?

Since averaging kills the transient part of the velocity, how does the momentum equation for URANS look like? Or do we average over a smaller time instead of infinity?

I would suggest that the problem is not computational power, but incorrect approach of the math. SpaceX is landing vertically, I suggest this was much harder to accomplish than determining the correct math approach to the issues presented here.

Imagine Just How Much Information Nature Is Caculating Every Minute Interval.

Where did the 2/3 k term come from? If I am not wrong such kind of a 2/3 term also exists in compressible NSE...

if we have P = rho R T, how can we use RANS to find P/Pavg = T/Tavg + rho / rhoavg?

Is there something I'm missing? For me this momentum equation is not dimensionally consistent

🙏🙏🙏

18:50 Dirac's delta? Buddy, that's the Kronecker delta

Srry I'm not an engineer but can use this for game dev in testing aircrafts and rockets in my game

How can it be so flowless?

10:56

Hello some one has the Lex Smith notes?

Kanisza Triangle.

I FEEL LIKE TO LISTEN YOU ALL THE TIME EATING SLEEPING WALKING