Talk:Reynolds stress

Thanks for this article! Some questions:
 * Should this be Reynold's stress or is it always plural?
 * I would like to add equations taking into account friction at siphon. How does this relate to a Reynold's number?  Samw 20:44, 8 May 2005 (UTC)

Hmm. It's just a thumbnail sketch of an article now, basically something I just wrote up over a glass of wine. Thanks for the interest!
 * Reynolds stress is the preferred usage -- that or Reynolds stress tensor. The usage "Reynold's stress" is incorrect because the stress is named for Osbourne Reynolds.
 * Turbulent friction (which may be thought of as being due to the Reynolds stress) is important in flow through pipe, i.e. pipe Poiseuille flow, at high Reynolds number. However, there is the question of what one means by "high", since there is actually no known linear instability that leads to turbulence in pipes. The breakdown is generally described phenomenologically, and the resultant loss of head is described by engineers with an effective friction factor. I don't know much else about it besides that, but I think that discussion of that is best left to discussion of specific flow scenarios/regimes such as pipe flow, rather than in the specific context of siphons. --Petwil 21:22, 11 May 2005 (UTC)
 * Perhaps it should be Reynolds' stress? 210.10.201.90 01:29, 9 October 2005 (UTC)

yes it should and I just moved Reynolds number to [Reynolds number]] Fegor 06:54, 5 September 2006 (UTC)

Eulerian Derivative
This may be a textbook thing but isn't D/Dt known as the Eulerian derivative, not the Lagrangian Derivative? This way makes the most sense to me since D/Dt came from using the Eulerian description to describe a particle's motion.

Just wanted to say thanks for the article. It was very useful to me.

And, as far as I can determine, D/Dt is usually called Substantial Derivative, or Material Derivative.

Hmm. Well, as I understand it the Eulerian derivative would be the derivative at an Eulerian point, which would be $$ \partial/ \partial t $$, whereas the Lagrangian derivative would be the derivative following an individual Lagrangian fluid "particle", and is thus D/Dt. That's my usage. "Substantial Derivative" and "Material Derivative" are fine as well, except that these terms are used primarily in the engineering and materials literature and are not common elsewhere. Most physicists call D/Dt the convective derivative. Finally, to keep from confusing this with motion driven by buoyancy, astronomers call it the advective derivative, which is my actual preference. And yet I have also encountered some people who use "advective derivative" to mean not the full D/Dt part, but just $$ v \cdot \nabla $$. So there is no good answer. Petwil 07:56, 19 May 2006 (UTC)

Fair enough. You seem to know more about this stuff than me anyway. Personally, I’ve always seen D/Dt called either “Material Derivative” or “Substantial Derivative”, but then I’m an engineer.

Come to think of it, “Lagrangian Derivative” does make more sense – after all, D/Dt is the derivative that you would obtained by following a particle. This seems odd to me, since D/Dt is the derivative of the Eulerian field. Hmm. But whatever you call it (and I would stick with Lagrangian Derivative), it is definitively not the Eulerian Derivative.

Anyway, great article. Care about writing one about the Reynolds-stress transport equations?

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I find this sentence confusing:

"A transport equation for the Reynolds stress may be found by taking the outer product of the fluid equations for the fluctuating velocity, with itself."

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 * Thanks for the comments. Yea, I guess that sentence is a bit confusing. I haven't been logging on to wikipedia for a while b/c I haven't really had time.... and hey, anybody else is welcome to edit this thing to make it read better. Anyway that passage would be made clearer by writing a separate page about Reynolds-stress transport equations, so I guess I'd better do that, but it'll have to wait until a few weeks from now when I have time. Or somebody else could write that page if they haven't already.Petwil 06:37, 8 September 2006 (UTC)

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This is what I have been looking for. I got a clear understanding of how to derive Reynolds stress from Navier-Stokes equation, but another question remains to me; Reynolds stress can be expressed with 'eddy viscosity' times gradient of velocity profile. I have some clue about this - Prandtl's mixing-length theory, abbreviated, MLT. However, I couldn't find any article that derivates eddy viscosity term as clearly as this one has done. So, I would appreciate it if you help me know how to derive eddy viscosity term from what equation or recommend a web article that deals with Prandtl's mixing-length theory in detail. —Preceding unsigned comment added by Closerefer (talk • contribs) 02:25, 17 December 2008 (UTC)