Talk:Reynolds-averaged Navier–Stokes equations

Osbourne Reynolds? (Fixed)

• I believe that this article would benefit a lot if it had a reference to the scientific author of the theory: Osborne Reynolds --Mecanismo 09:15, 4 October 2005 (UTC)

Done. Added reference to Osborne Reynolds, and introduced Reynolds decomposition concept, into the introduction. --Charlesreid1 (talk) 04:06, 6 November 2010 (UTC)

• The articles in which Reynolds developed the idea of decomposition into mean and fluctuating components is in Vol. 3, section V of "Papers on Mechanical and Physical Subjects" published by Cambridge University Press in 1903. — Preceding unsigned comment added by 76.216.200.102 (talk) 02:57, 1 October 2012 (UTC)

Einstein summation convention

• Maybe it would be helpful for beginners to mention somewhere that the Einstein summation convention is employed throughout the article? - Erik

I briefly added that just before the RANS equation definition, should be helpful to beginners I think. MasterHD (talk) 22:26, 12 April 2010 (UTC)

Time average vs. Ensemble average

I think that speaking in terms of Time average when dealing with Reynolds equations is not correct in principle. As far as I know, for the Reynolds decomposition to make (theoretical) sense, average must be considered as an ensemble average.

Time average (or even volume average) and ensemble average concide only when the flow is statistically steady, which means that

${\frac {\partial {\overline {u}}}{\partial t}}=0$

and that makes Reynolds equations time independent, which is not the case.

In practice, time average is performed in data analysis assuming that the averaging interval is much shorter than the typical scale of statistical unsteadiness. This allows to approximate the ensemble average with the time average (the same holds in space). This is related to the ergodic hypothesis.

However, because the author seems to be convinced of the contrary, I would like to discuss this fact to make someone convince me that I am wrong, before editing this (and related) articles.

Please sign your comments. --Charlesreid1 (talk)

Well, I agree with you. I started the article, and talked about time averaging and 'applicable to steady flows', because like you say thats how Ive used it in practice. I say go ahead, change what you need to and include relevant parts of your discussion in the article. Maybe "the author" is a bit of a misnomer on wikipedia, but yeah someone did add a bit about "Ensemble averaging is not the same as Reynolds averaging" which confused me. Dougalc 22:02, 7 May 2006 (UTC)

The flow does not need to be steady to take a time average, you just need the period ${\Delta }t$ of the average to be appropriate length so that you can resolve the fluctuations into a value separate from the mean. Then it follows that $u^{\prime }=u-{\bar {u}}$, from this definition of the time average:

${\bar {u_{i}}}\equiv {\frac {1}{{\Delta }t}}\int _{t_{o}}^{t_{o}+{\Delta }t}u_{i}dt$

The mean is allowed to change over time, it should encompass the larger scale unsteady flow features. MasterHD (talk) 22:09, 12 April 2010 (UTC)

Ref. for the above: C. Hirsch "Numerical computation of internal and external flows - Fundamentals of numerical discretization" (volume 1) Pages 49-51, ISBN 0471 91762 1 146.87.52.53 (talk) 00:27, 1 May 2012 (UTC) Anon.

Expansion badly needed

Article is badly in need of expansion. Information about turbulent scales being modeled, mention of unsteady RANS, $k-\epsilon$ and $k-\omega$ models, and at least SOME references (there are literally hundreds out there) should be cited. --Charlesreid1 (talk) 04:13, 6 November 2010 (UTC)