Can someone please explain the concept of circulation? I am able to understand the mathematical form i.e. it is the line integral of the velocity field. But I am not able to understand the physical meaning of circulation.

  • $\begingroup$ It has been explained to me that this concept of circulation is purely a mathematical concept. But, I look forward to some clarification on this because diagrams showing forward flow on the bottom surface of the wing don't lend themselves to aiding understanding of actual flight. $\endgroup$ Oct 22, 2019 at 16:10
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    $\begingroup$ You may read how it flies? which is an excellent resource to understand basics about aerodynamic of an aircraft. $\endgroup$
    – Manu H
    Oct 22, 2019 at 17:04
  • $\begingroup$ @Gerry, that's the one I was thinking about, thanks! $\endgroup$ Oct 22, 2019 at 17:34
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    $\begingroup$ Do the answers in the other question resolve your understanding? Or do you need further clarification? $\endgroup$
    – JZYL
    Oct 22, 2019 at 19:15
  • $\begingroup$ @Gerry I think this question could be considered a duplicate of the one you linked to. I thought Pilothead's answer was a pretty good description of the concept in terms a layperson would understand. $\endgroup$
    – John K
    Oct 22, 2019 at 20:29

2 Answers 2


Circulation does not mean that any fluid particular is traveling in a circuit around the airfoil. One way to look at circulation is that it's a description of how much a uniform flow has been turned asymmetrically by the body.

Another, slightly more technical way, is to consider the flow around a rotating cylinder (which produces lift) as a combinatory sum of a uniform flow (free-stream flow), a doublet flow (non-lifting) and a vortex flow (which produces circulation). See this illustration excerpt from Anderson, Fundamentals of Aerodynamics.

Lifting Flow over a Cylinder

Therefore, circulation can be regarded as the path of the fluid when the symmetrical components have been taken out, which is indeed circuitous.


I found this truly ancient video quite helpful when I was trying to comprehend the concept of circulation.

Now, I have no idea whether my intepretation is righ, but I would describe the circulation as the motion particles of air in the path of an airfoil make as the airfoil passes by them.

This effect can be seen in the last 30 seconds of the video.

The trick is to change coordinate system: Instead of looking at the flow of air from the perspective of an airfoil, you should look at the flow of the airfoil from the perspective of the particles of air.

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    $\begingroup$ The video shows an airfoil shedding vortices, but that has little to do with the main question, that might be stated as follows: Does a speck of dust caught in the midst of that 'circulation', really revolves round the wing...? or is the Kutta-Joukowski circulation just a useful mathematical construction...? $\endgroup$
    – xxavier
    Oct 22, 2019 at 19:14
  • $\begingroup$ I don't think that the Kutta-Joukowski circulation model is useful or practical. It seems like an abstraction to me. $\endgroup$ Oct 22, 2019 at 20:10
  • $\begingroup$ Yes, the airfoil does shed vortices as it starts to move and as it stop in the end of the video, but what I was referring to, was the movement of a particle as the airfoil passes by it, forcing it to move. This movement is, if not completely, then very close to circular. $\endgroup$
    – Jpe61
    Oct 22, 2019 at 20:13
  • $\begingroup$ @MichaelHall All the important analytical results in aerodynamics is derived from Kutta-Joukowski...I don't know why you would say it's "impractical" $\endgroup$
    – JZYL
    Oct 22, 2019 at 20:29
  • $\begingroup$ @Jpe61 - I don't see any point at which particles circulate forward along the lower edge of an airfoil that is moving through the airmass. $\endgroup$ Oct 22, 2019 at 20:31

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