# Talk:Vorticity

## Biot-Savart?

How is Biot-Savart a part of fluid dynamics? —Preceding unsigned comment added by 18.218.1.100 (talk) 23:59, 8 September 2007 (UTC)

Used to evaluate flow due to a system of vortices - see say Horseshoe vortex of a wing, or thin-airfoil theory. Bob aka Linuxlad 14:04, 9 September 2007 (UTC)

## Edit wars and others

(William M. Connolley 19:16, 25 Jun 2004 (UTC)) I've made some minor changes, and also removed the ref (and hence its section). This needs justifiying. The justification is twofold: firstly the ref'd defn isn't very good. But more importantly, the ref def doesn't include anything that isn't in the wiki article. So there is no point in referring people to it: they will learn nothing new. If its there to bolster claims in the edit war, it belongs here on the talk page and we'll discuss it: but still not on the article page.

As to the edit war: vorticity *is* its definition. Its not a natural-language word. If the definition is difficult or confusing then some text trying to explain it may help. But in that case you have to be very careful that the explanatory text is accurate.

## Pmurray bigpond.com 23:20, 22 February 2006 (UTC)

The article mentions "vorticity" moving from place to place. Is this related to the conservation of angular momentum? It might be worthwhile mentioning it if so. I suppose that angular momentum density would be equal to the vorticity times the density of the fluid or something.

There is indeed a close relation between the two ideas, because ω is twice the local angular rotation rate. So the angular momentum of a small spherical blob in the fluid, of moment of inertia I, is (0.5 I ω) (see Batchelor eqn 2.3.12 & 5.2.2). But you'ld need to keep tabs on I, as the fluid distorts, as well as ω. The constancy of the strength of a (small circular) vortex-tube in inviscid flow is essentially a statement of the conservation of the angular momentum within it (see Batchelor, eq 5.3.4). Linuxlad 09:55, 23 February 2006 (UTC)

## Misprint or my bug?

Somewhat counter-intuitively, an irrotational fluid can have a non-zero angular velocity (e.g. a fluid rotating around an axis with its angular velocity inversely proportional to the distance to the axis has a zero vorticity)

It should probably be azimuthal velocity. For a simple cylindrical rotating case rot V = 1/r*(d(r V_phi)/dr ). When V_phi=1/r then rot V = 0.

I'm not changing the page because I may be wrong but still check this out, pls.

Best regards, Step.

Yes it's rv=constant in a 'free vortex'. The description of forced and free vortices in vortex uses the term 'tangential velocity' which may be preferable to 'azimuthal' (which suggests angular rather than linear measure). Linuxlad 12:57, 9 March 2006 (UTC)

Yep, I agree. 'Tangential' seems to be the correct word there... Although not to introduce linear velocity at all it may be better just to change

(e.g. a fluid rotating around an axis with its angular velocity inversely proportional to the distance to the axis has a zero vorticity)

to

(e.g. a fluid rotating around an axis with its angular velocity inversely proportional to the square of the distance to the axis has a zero vorticity)

or something like that.

--194.85.80.92 18:54, 9 March 2006 (UTC)

I have no comment on 'tangential' vs. 'azimuthal' vs. 'angular'. I find the first part of the statement unnecessarily confusing. The local angular velocity of a fluid blob about its own axis is always zero in an irrotational fluid, but its angular velocity about some other axis may be nonzero. There's nothing counter-intuitive about it. -I.G. — Preceding unsigned comment added by 69.117.114.222 (talk) 19:54, 4 November 2011 (UTC)

## Southern Hemisphere vorticity

In the atmospheric sciences, vorticity is the rotation of air around a vertical axis. In the Northern Hemisphere, vorticity is positive for counter-clockwise (i.e. cyclonic) rotation, and negative for clockwise (i.e. anti-cyclonic) rotation. It is the same in the Southern Hemisphere although the rotational direction differs to that in the Northern Hemisphere.

These sentences seem confusing to me for the Southern Hemisphere consideration. Is vorticity positive for counter-clockwise rotation (anti-cyclonic) or for clockwise (cyclonic) rotation? --User:ludooohhh 08 October 2007

Done. Dolphin51 22:32, 13 November 2007 (UTC)

## Zeta v. omega

Does this article change between using omega in the main section and zeta in the "atmospheric sciences" section to represent vorticity? Is there a reason for this? I am used to seeing zeta, as to distinguish it from the angular velocity omega. 68.151.166.14 (talk) 04:50, 7 October 2008 (UTC)

I agree that two symbols are used for vorticity in this article - omega (${\displaystyle \omega }$) and zeta (${\displaystyle \zeta }$). I believe it is almost universal for zeta to be used because the vorticity of a small fluid element can be shown to be twice the angular velocity of that element, and the universal symbol for angular velocity is omega. The article is conspicuously lacking references and in-line citations (except for the meteorology topic) so we have no idea whether omega is used for vorticity in any reputable source document, or whether it was an oversight on the part of the original editor. I will change the symbol to ${\displaystyle \zeta }$ and support it with an in-line citation. If anyone objects they will be free to revert to ${\displaystyle \omega }$ if they can provide an in-line citation to support the reversion. Dolphin51 (talk) 22:07, 8 October 2008 (UTC)
I strongly recommend changing the symbol for vorticity to omega. In my experience, I have never seen the symbol zeta being used. Omega has been widely used in publications and journal articles. The Wolfram Scienceworld page in the references section of the article uses omega, and so does the book Vortex Dynamics by P G Saffman, which is widely used as a standard textbook for the subject. As for angular velocity, in fluid dynamics it is represented by the uppercase omega symbol. I believe the usage of zeta might confuse new readers. The Raytracer (talk) 13:17, 11 October 2008 (UTC)
Hi Raytracer. Thanks for joining the debate. The debate began when 68.151.166.14 drew our attention to the fact that the article Vorticity contained a mixture of omega and zeta. Omega was used uniformly throughout the general treatment of vorticity; and zeta was used uniformly throughout the section on atmospheric sciences. (Now that IS confusing!) Not one in-line citation was used in the article to show the sources of the information on which the article was based. I provided an in-line citation to Clancy's book Aerodynamics (which uses zeta for vorticity, and omega for angular velocity.)
In Wikipedia, the article Angular velocity states that the symbol for angular velocity can be either upper case omega, or lower case omega. It doesn't reflect your view that in fluid dynamics, angular velocity is represented by the uppercase omega. The article Vorticity equation also uses a confusing mix of zeta, eta and omega.
I suggest you add a statement showing that the symbols used for vorticity are either zeta or omega. As an in-line citation for omega, you could quote Saffman. Dolphin51 (talk) 10:46, 12 October 2008 (UTC)
Both my dust-covered tomes, Kay & Nedderman (Fluid Mechanics & transfer processes), and Batchelor (Intro to Fluid Dynamics) use lower-case omega. Bob aka Linuxlad (talk) 15:24, 12 October 2008 (UTC)

## Vorticity SI Units?

Does anyone know of the standard Metric SI units for Vorticity? This should be mentioned in the article. --70.48.52.77 (talk) 16:04, 20 October 2008 (UTC)

The vorticity of a small parcel of fluid is twice the angular velocity of that small parcel. Angular velocity can be measured in revolutions per minute but is more commonly measured in radians per second. The unit of measurement of vorticity in the SI system is also radians per second. The most significant thing about vorticity is that just about everywhere in a fluid flow field the vorticity is zero, and therefore it requires no units of measurement. It is only in places such as the boundary layer and in the core of a vortex that vorticity is non-zero. Dolphin51 (talk) 01:13, 22 October 2008 (UTC)

## Quantized vortex lines

Surely (especially since vortex line redirects here) there ought to be some mention of quantized vortex lines, as seen in superfluids? A.C. Norman (talk) 13:26, 23 July 2009 (UTC)

Feel free to write something on quantized vortex lines, especially if you are able to provide an in-line citation to show the source of your information. You could add some text directly to the article, or place your text on this Discussion page and ask other interested Users for comment. Dolphin51 (talk) 23:10, 23 July 2009 (UTC)

## Absolute and Relative examples misleading

I think many people will find it confusing that there is so little scale variation on the figures showing 'absolutre velocity'. Couldn't we remake them so you can actually see some variation on them corresponding to the relative ones? — Preceding unsigned comment added by 138.37.50.7 (talk) 12:42, 25 February 2013 (UTC)

I second this. I'm not sure there is any variation in the absolute images.

173.25.54.191 (talk) 04:17, 15 March 2013 (UTC)

I think an explanation of what is meant by relative velocity should also be included. Eyrryds (talk) 17:49, 1 April 2013 (UTC)