Turbulence: Reynolds Averaged Navier Stokes (RANS) Equations (Part 2, Momentum Equation)

[@henryginn7490]

This was fantastic. Self contained, clear thought put into the target audience, and the steps were well motivated. These two videos aren't just a derivation, they give you the understanding and context behind the model. The effort put into the narrative and pedagogy in this video are certainly appreciated.

[@JousefM]

You know the lecture is getting intense when you can barely see Steve through the glass :D

[@Eigensteve]

I was getting worried towards the end there!

[@muratcan4624]

@@Eigensteve you literally spoke through an open gap between Reynolds stresses :)

[@wazirakbar1218]

Dear Dr. Steve, You are making me change my research area in the last year of my PhD. I really love your lectures. I even watched your full lectures ME564 AND 565, just for fun. A great teacher you are. keep it up. God Bless you.

[@a.e6328]

Thanks Steve. I'm very excited to see more focus on turbulence. I'm from a different field, I mainly do measurements of atmospheric fluxes in the boundary layer and these videos are very helpful to get into the math of turbulence.

[@Eigensteve]

Thanks! Looking forward to making the next few vids.

[@mro6030]

Thank you for this series on turbulence, Steven! I started when it all begun but got busy, and I am finally catching up this weekend! I feel there is so much to be done in the field or turbulence simulations, this is definitely making get our of my comfort zone and finally finish writing my proposal and start applying for a PhD! Thank you for the inspiration!

[@itetecnun]

This content is really great quality. Thank you very much for sharing. It is really hard to find quality content related to this topics in the web, explained this good.

[@abrahamsilas2204]

Thanks Steve for the lectures. It's always lovely listening to your lectures.

[@Eigensteve]

Awesome, glad you like them!

[@abrahamsilas2204]

@@Eigensteve Yes I like your lectures beginning with the control bootcamp to HAVOK, SINDy, SVD, etc etc. I wish I have an opportunity to ask a few questions on SVD and, maybe a couple more things. The example you used on lectures on SVD was, I believe, Over-determined system (I really hope I got it correctly.) My current research is on Under-determined system and I'm hoping I'd get the results I'm expecting. If it'd not be too much to ask I'd appreciate if I have a little time of personal conversation with you. If it's okay by you I could have your email address. My email is [e-mail]. Thank you so much. I love you, Steve.

[@satyapratapnayak4853]

Thx sir ...im from india ...its really cleared my doubt.....now i can move forward to focus on my research paper on rocket nozzle flow separation 🙏🙏🙏😍😍

[@ssss4391]

Amazing lecture. A correction required in the velocity decomposition: U_average should be divided by T, otherwise the limit will be infinite even for a constant velocity.

[@Eigensteve]

Good catch, thanks!

[@vanchhitdubey]

Thank you so much prof. Steve, I found your channel by surfing for RANS modeling and got to know that you are doing ML models for the same. I am going to start a ML project for jet Combustion, It would be a nice journey of learning with you.

[@arungandhi5612]

eagerly waiting for this amazing content , you make my phd easy

[@prestonr6348]

Hi Dr. Steve I'm not sure but I think 16:33 should be written as (dv'/dy)u' instead of (du'/dy)v'

[@LucasDimoveo]

Kale and deadlifts pretty good ngl 🥬 Excellent video as always

[@Eigensteve]

I know, that is my secret.. I love kale :)

[@LucasDimoveo]

@@Eigensteve if you haven't already tried it - chard and collard greens are also fantastic. Sauteed with coconut aminos and some curry spices

[@mohamednasser2725]

WOW! It was a very good lecture and I'm looking forward to seeing what's coming.

[@giampietrobusi]

Thank you, really clear and appreciated your approach to write the equation for just one component helped me tremendously learning this subject, my professor went pretty fly over this, hope this will help me in my exam tomorrow. Sorry for the english, i'm not native :)

[@diliniherath1299]

And I know we all like Kale ! 😝 Wonderful lecture as always ! Thanks 😀

[@abdallahaithammou1327]

Hey Dr. Brunton, can you explain why did you take the mean of the equation per minute 8:59 thank you

[@khaldrogo98]

Thanks Dr. Steve!

[@Ethan-mi1wj]

Where are the continuation lectures on this topic?! I really need them

[@jjamongtea]

Dr. Brunton.. I always appreciate your lecture. more than words.. Would you provide a lecture on k-epsilon model following Part 2 momentum equation?

[@turbochargersutututu]

This is such a life saver! Thanks so much! Can you possibly do a lecture on unsteady RANS (URANS), where an ensemble average term is included please? I cant find any place where the math behind that is explained clearly.

[@m0nzderr1]

Steve, great lecture! Although, there is one thing: the notation of U_x, U_y, U_z and p_x that just got me confused. I had to stop for a moment to realize that U_x = \partial U / \partial x and so forth.

[@nebiyubogalemereke9214]

Thank you! you make my life easier.

[@motster33]

2:44 how can those partial derivatives not have a term on the top and only the d?

[@Topakhok]

I think you made a small mistake there (at 8:45). u’_t bar is equal to zero not because of the fifth rule (it applies only to space derivatives), but just as a matter of a simple calculation. Integral of a derivative gives you the difference of velocities and then you divide by big T (which goes to infinity) and in the limit you get zero :)

[@SachinBharadwajManjunath]

Dear Prof. Steve, I am a huge fan of your lectures. Thank you for this video on derivation of RANS equation. My doubt is - Why do we make temporal derivative of time average of velocity equal to 0? Is it 0 only when the turbulence is statistically stationary or even if the turbulence is periodic or intermittent in nature?

[@uyvu560]

Hi Sir, I have a very important question that are you writing by the Left or Right hand?

[@AP-ei8iw]

wonderful, wonderful, wonderful, I have searched everywhere this topic and got here only. Perfectly explained. How can I contact you if I have any doubt ?

[@mohammadfozankhan4242]

Hi Dr. Steve, Very informative and insightful. Thank you so much. :-)

[@marcelloceresini1810]

I've been looking for weeks now for some papers that help CFD solvers through use of AI. I think I remember you talking about sparse computation that is then "filled" through the means of an AI model, but I have been unable to find the video in which you talk about it (if it exists..). Could anybody help me with some content about that? Sources, papers, anything you have. Thanks in advance

[@apocalypt0723]

Amazing video. Thank you for this.

[@xo29.01]

Quality teaching

[@jonascosta7615]

Amazing class!!!

[@drskelebone]

Sorry, but what class would this be? I never had this in my [redacted] years of physics. Is this an engineering thing, or is this something you'd get if your thesis advisor did fluid dynamics?

[@husseinsleiman6119]

Thank you for this amazing lecture. I have a small question and hope you can answer me. I was wondering in the mean average term in the Reynolds decomposition equation why does the mean average velocity is only a function of x and not x and time (x,t)? I have seen a book that it is written u(x,t)=u_bar(x,t) + u_prime(x,t). If that was the case, can you still assume the U_bar(t) is zero?

[@science_engineering]

why do we average of the equtions? does this mean that on such a way we get only a stationary solution? what i'm more confused about is why we are doing time averaging in RANS without assumption that turbulence is ergodic... As I understood correctly, even though turbulence (e.g. velocity) stationary, it doesn't mean that the turblunce is ergodic. Hence, we are allowed to do ensemble average only, not time average.

[@mulligatawnysoup6722]

If the flow is "drifting" in time, .ie. the mean is steadily changing, wouldn't that give a non-zero Reynolds stress even if there was no turbulence?

[@WilliamDye-willdye]

1:58 "I know that we all love kale". Actually I do love kale, but I thought I was a weirdo. Oh, well. Back to the way-cool equations.

[@Eigensteve]

:)

[@1729krish]

One silly question: Why is average of (u'*v') not 0 when each of these terms averages to 0?

[@lucaswarwaruk36]

Hey Dr. Brunton, great video and video series! Quick question: can you please clarify why you removed the unsteady term from the RANS equation? I thought generally this would be non-zero (see Pope, S.B., 2000 Turbulent Flows 4th edition, chapter 4, p. 84). That being said, neglecting the unsteady term makes sense to me with regards to physical Reynolds averaging of say experimental data. That is, you take the mean over all samples in time and even if there are dominant secondary unsteady flow patterns, they get averaged all together (ex. Reynolds averaging measurements of a turbulent wake flow with a vortex street). Could there be some moving time average that captures the unsteadiness of the mean flow pattern? I'm curious why Pope maintains this term.

[@clickingbuttons1886]

Hey. Not as knowledgeable as Prof. Brunton but I can try my explanation. RANS tries to squeeze the unsteady flow into a steady solution and the time derivative is not solved. There is something called Unsteady RANS (URANS) that discretizes the time derivative similar to other numerical methods such as LES. This one is able to capture the unsteadiness of mostly large-scale vortices such as the famous von Karman vortex street.

[@koriye6668]

I think Clicking Buttons is correct. I saw on p. 83 Pope keeps his average velocity a function of both position and time rather than being a function of position only. So it seems like this provides a more general solution. If your mean velocity is time averaged over your entire sampling interval, then it would become time invariant, and setting its time rate of change to zero makes sense.

[@ru2yaz33]

Now with the characteristic length scale...

[@iaeroespacial]

Thank you!

[@2ednar739]

What is the camera setup here? Are you writing on a window? Just super curious 😲

[@drumbum7999]

he writes on glass and then the video is mirrored about the vertical in post so the text is legible to the audience. He's smart but I don't think he's do-this-entire-derivation-while-writing-in-reverse smart.

[@bryanblaise79]

Does anybody know what technology he uses to write? What is he writing on/writing with/what software he uses?

[@Topakhok]

I saw other guys doing that. They just write on a big piece of glass, the ordinary camera shoots them and then the image is flipped horizontally

[@hari.santoso]

Yeah. Right. But, how to solve the equations?

[@chizhang3263]

cool guy teaching cool stuff. Sadly UW rejected me :( otherwise I am probably taking your classes.

[@mohamedelaminenehar333]

❤😊✌ Tge best steve in history

[@ireoluwaTH]

Yelling through the screen... Ooops - there was nothing wrong!

[@pawankumar-ir1fd]

best

[@firstcommenter202]

not chain rule but product rule

[@rat_king-]

Very drunk me, I CAN SOLVE IT..... fails passes out immediately

[@sososoawesome1]

no idea what's going on, ill just memorise the steps