Talk:Cascade and scaling

Reviewer A

This is a very nice summary of the themes of turbulent cascades.

Minor comments:

1. Line -5 of the first section. Maybe it would be better to add around \(P(v,r)=f(v/r^\alpha)/v\) that \(f\) envolves outer and/or inner scales to hint on why the equation may be dimensionally correct. (Falkovich: No, this is likely to make reading more diffcult, April 03, 2008)

2. Line 8 in the Burgers section. "...at the limit \(_{\nu\to0}...\)" should better be "...in the limit \(\nu\to0\)" and similarly in other places. The last "then" in the same line should better be capitalized. (Edited by Nwerneck 21:03, 31 March 2008 (EDT))

3. 12 lines below, the equation \(P(w,x)=w^{-1}f_1(w u/x)+xf_2(w/u_{\rm rms})\) has in it \(u\) and \(u_{\rm rms}\) which should be explained or, better, dropped. (corrected, Falkovich 03 April 2008)

4. 6 lines below, it should be mentioned what \(L\) is. (it is defined, Falkovich 03 April 2008)

5. In the second line passive scalar section, both \(\varphi\) and \(\phi\) are used for the same quantity.

• I changed all four \varphi do \phi (31 March 2008), but then the author took it back, leaving the same (fifth) \phi as such. Is it really supposed to be that then?... -- Nwerneck 22:29, 4 April 2008 (EDT)

6. In the line after the formula for the scalar 2-point function, one expression (for \(\Phi\)) does not show correctly. Also, \(R_{12}\) and \(r_{12}\) here and below, should not be bold.

• Edited by Nwerneck 21:03, 31 March 2008 (EDT). I suppose the problem was the large parenthesis. Fixed that.
• I believe the author does prefer the bold version. -- Nwerneck 22:29, 4 April 2008 (EDT)

7. The statement in the first line of the Navier-Stokes section is, at least, disputable and should be weakened. (done, Falkovich 03 April 2008)

8. Line -5 from the end of the main text. The use of the formula \((*)\) in the inverse scalar cascade is somewhat abusive because the time integral diverges in the \(-\infty\) limit and the 2-point function grows also in time. (corrected, Falkovich 03 April 2008)

Equilibrium

There is an autolink to “equilibrium” in the article, but it doesn't seem to me that this is a proper link for “thermal equilibrium”... What should we do: just nowikify the equilibrium; point to an inexistent “thermal equilibrium” article, or another article; or suggest the inclusion of something about thermal equilibrium in the equilibrium article? -- Nwerneck 18:00, 9 March 2008 (EDT) (Nwerneck 21:05, 31 March 2008 (EDT))

Large Image

This first image is huge, and it's taking long to load the thumbnail. Is it Scholarpedia's server who is slowing down the scaling process?... Are there any server configurations we can tweak? Or is it just the way we want right now (while we don't have a server larger then Google's)?... -- Nwerneck 18:12, 9 March 2008 (EDT)

I converted the image to jpeg; it is only 86K and loads faster. Eugene.(Nwerneck 21:05, 31 March 2008 (EDT))

User 1 (Assistant Editor): Introduction and definition

I believe a small introductory paragraph at the beginning is desirable. -- Nwerneck 01:29, 28 March 2008 (EDT)