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

Turbulent fluid dynamics are often too complex to model every detail. Instead, we tend to model bulk quantities and low-resolution approximations. To remain physical, these reduced approximations of the Navier-Stokes equations must be "closed", and turbulence closure modeling is one of the most important topics in high-performance computing and scientific computing. This video describes several leading approaches, including the Reynolds averaged Navier Stokes (RANS) equations and large eddy simulations (LES).

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This video was produced at the University of Washington

[joaquinparedes]

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.

[michaelmello]

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

[KidneyBicep]

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.

[lenmargolin]

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.

[marquisote]

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!

[faroukhasnaoui]

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

[snneossi]

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

[aliasghar_mech_eng]

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

[curtisrichards]

You explain this better then my professor at UCF.

[sramkumar]

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

[cedarcreekstackleshop]

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! :)

[johnpayne]

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.

[mariovrpereira]

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

[anantdiwakar]

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.

[lioneloddo]

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.

[beaceelkebeer]

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

[iuliana_swetty]

Thank you, you're way better than our professor called Mr. Bioche. He's incompetent in my book. Thank you again my man appreciate it.

[AP-eiiw]

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

[闫建东]

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

[anurajmaurya]

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