Talk:D'Alembert's paradox

Talk page archive

Archive 1 has been created with a link at above right. It is an exact copy of the talk page as it was before this edit (besides the last two sections which I left here). Archive 2, when needed in the future, should be a new subpage (same as creating an article) titled "Talk:D'Alembert's paradox/Archive 2" and the link added to the template on this page's code. For further information on archiving see Wikipedia:How to archive a talk page. See also User:5Q5 for the used archiving procedure. Thank you. -- Crowsnest (talk) 23:08, 9 April 2009 (UTC)

misleading diagram

Streamlines for the potential flow around a circular cylinder in a uniform onflow.

I think this diagram captioned "Streamlines for the potential flow around a circular cylinder in a uniform onflow." is misleading. Physical cylinders never have streamlines that look like that. I think it would be better if this picture were re-labeled to emphasize that this is "merely" what the mathematical equations predict, and another diagram placed against it -- in a similar artistic style -- that shows the real streamlines around a real circular cylinder. Perhaps somewhat like the 2 similar diagrams in the aerospaceweb: "Golf Ball Dimples & Drag" article.

I think 2 contradictory diagrams would help make it more obvious that the d'Alembert's Paradox is the contradiction between theory predicts this, but experiments in real wind-tunnels show that. --68.0.124.33 (talk) 04:11, 14 November 2008 (UTC)

New resolution published in Journal of Mathematical Fluid Mechanics

A resolution of the paradox was published on Dec 10 2008 in Journal of Mathematical Fluid Mechanics, the leading journal on theoretical and computational fluid mechanics based on mathematics. CS is actively suppressing this information and thus actively suppressing material published in a leading scientific journal. CS has to carefully motivate this censorship exercised by someone with unknown name and scientific merits. Come out of the cage and motivate the suppression! Egbertus (talk) 09:01, 14 December 2008 (UTC)

Peer review

I have raised this article from Start Class to B Class. The article has matured substantially in the past year and it may even qualify for A Class.

I believe the time has come for serious peer review of the article, firstly to confirm that it is genuinely of B Class quality, and secondly to determine the extent of agreement that it might already be of A Class quality. Information about the various quality classes, and the criteria that apply to each class, is available at WP:ASSESS. Dolphin51 (talk) 02:30, 15 April 2009 (UTC)

Loss of boundary condition when viscosity EXACTLY equals zero

I know there has been a LOT of detailed discussion in the archive. I admit that I have not read it all in excruciating detail. But I did read quite a bit and I don't think the point below was quite made.

There is an interesting observation about the forms of the NS equations and Euler equations which might give some additional insight. The viscosity appears in the coefficient of the second order derivatives in the NS equations. If the viscosity is identically zero, then the the second order terms vanish and the equations reduce to the Euler equations. If the order of the equation drops by one, then one loses a boundary condition (i.e., the no-slip condition). If viscosity merely APPROACHES zero, then the NS equations remain second order and the no-slip condition can still be applied.

This means that the NS equations do not APPROACH the Euler equations as viscosity APPROACHES zero. The NS equations only BECOME the Euler equations when viscosity EQUALS zero identically.

Thinking about it physically instead, as viscosity decreases, the boundary layer gets thinner. The forces within the boundary layer will always act such that the viscous and inertial effects will be of comparable magnitude. It is exactly that balance of forces that leads to the thickness of the boundary layer in the first place. Thus, if you constructs a Reynolds number based on the boundary layer thickness, then that Re will remain essentially constant despite viscosity approaching zero. So within the boundary layer, viscosity is always important, no matter how small it gets.

The low velocity fluid at the bottom of the boundary layer cannot withstand adverse pressure gradients (that are due to the flow around the body and external to the boundary layer) and separation will occur. This separation significantly alters the external flow. With ZERO viscosity, the flow velocity near the surface is large and CAN withstand the adverse pressure gradient. The fluid converts its kinetic energy into potential energy (i.e. pressure) towards the rear stagnation point and everything balances out beautifully.

With zero viscosity you get the potential flow solution. With infinitesimal viscosity, you do not. You get separated flow instead.

By the way, in all this, I'm talking about truly continuum mechanics. In rarefied flow, you do get slip at the boundary, but you have also violated assumptions that led to the NS equations.

And do I have references for all this? Well, no, not really. I'm hoping it's sort of self-evident once it's pointed out. This is stuff you already know. It's just put together in an interesting way. I didn't invent this either. My reference for this is personal communication. I'm just paraphrasing what was explained to me by my professors in the Aero department at Caltech 25-30 years ago. But I don't remember exactly who it was, so I can't even properly cite personal communication. It might have been Hans W. Liepmann, but I don't think so. I just audited his introductory fluids class after having skipped it in the beginning and gone straight to the more advanced class. It might have been Anatol Roshko, but I don't think so either. It's more likely I discussed the drag crisis with him. (We should really put together a page on that topic too. Well, OK, there is a page on that, but it's an orphan with one paragraph.) Most likely it was Don Coles who pointed out this business about reducing the order of the equation and losing the no slip condition as a result. He taught the advanced fluid dynamics class and was most likely to have formulated this sort of explanation. He placed great emphasis on dimensional analysis too. He does not have his own page here in Wikipedia, but he does appear as a recipient of the Otto Laporte Award in 1996.

Kimaaron (talk) 05:09, 11 September 2009 (UTC)

No Lift as Well

Many standard textbooks indicate that the paradox is not limited to drag. Rather, it claims that that for a perfect fluid, neither drag nor lift can be accomplished by a steady flow. —Preceding unsigned comment added by 76.104.101.94 (talk) 05:47, 12 September 2010 (UTC)

For a cylinder of infinite length, lift in a steady flow can easily be generated by adding a vortex singularity (located inside the cylinder) to a uniform on-flow. -- Crowsnest (talk) 20:22, 15 September 2010 (UTC)

Massless medium?

Hello. I have an idea that the paradox may be clarified by delineating two cases: one where the medium has mass, and one where it does not.

If the medium has mass, then despite this medium being inviscid (which I am taking, possibly in error, to mean "frictionless"), a moving body will encounter some resistance, because the medium must accelerate before the body can occupy a new position. The mass therefore acts as a false viscosity (or is it actual viscosity?) and creates a false drag (which, again, might be actual).

However, a massless medium would not exert an opposing force, because it can accelerate with minimal effort. The only way to even determine the presence of such a medium is to try and fail to compress an airtight (or medium-tight) container. --Bryce Herdt, 76.25.100.146 (talk) 21:19, 22 January 2011 (UTC)

Sorry to disappoint you, but d'Alembert's paradox is for media with mass. The medium (with potential flow) accelerates at the front and de-accelerates at the rear of the body, net resulting in zero drag on the body. It is easiest seen for potential flow around a circular cylinder, where the flow at the front and the rear is symmetric in potential flow (unlike the situation for a real flow, see e.g. Kármán vortex street).

Further, notice that this talk page is for discussing improvements of the article itself (see page top); you can ask questions about the topic at the Wikipedia:Reference desk/Science. -- Crowsnest (talk) 12:48, 23 January 2011 (UTC)