Aero is not my speciality at all so apologies if missed anything. But when looking at potential flows, i thought the whole point is for there to be no rotation at any point and its that reason the velocity can be described by a scalar fuction at any point, yet the vortex flow has a point of curl in the center and hence circulation. I noticed in J.D Andersons aero book that it is this particular flow that allows for lift in invicid flow which greatly confuses me further. Is there some hidden explination behing the vortex element?

Appreciate the comments.


1 Answer 1


A point vortex is a singularity: it's a zero-volume model of a rotational region of the flow. If you try to evaluate the vorticity in the singularity (or in some of its regularized forms), you get infinite vorticity.

Point vortex, line vortex or sheet vortex are usually a good model in aerodynamics, in the cases where vorticity is concentrated in thin regions: large Reyndols number, streamlined bodies at moderate angles of incidence usually implies thin boundary layers and free wakes.

In the mathematical model of the flow, vorticity of the boundary layers and wakes is lumped in singularities, while the flow is everywhere else irrotational.

  • $\begingroup$ Thankyou, but im still confused how this can be used in potential flow if potential flow only holds for all areas of 0 vorticity? $\endgroup$ Oct 23, 2023 at 15:44
  • $\begingroup$ The assumption of potential flow may hold only in some regions of the domain: if vorticity is zero in connected regions of the space, you can assume that the flow is potential in this very region. If you know where the vorticity is, you're ok. If vorticity regions evolve in the domain, you need to track them, usually through convection $\endgroup$
    – basics
    Oct 23, 2023 at 19:12
  • $\begingroup$ Thanks, so if it’s actually is truly inviscid can the vortex element occur? Because it seems the lift can be generated from this element because of the circulation, yet I thought lift and drag were not possible in inviscid flow? $\endgroup$ Oct 24, 2023 at 21:17
  • $\begingroup$ Both lift and drag are possible: if you're thinking at D'Alembert paradox, it deals with no drag in 2D steady inviscid irrotational flows only. For vortex dynamics, take a look at Helmhotz theorems, en.wikipedia.org/wiki/Helmholtz%27s_theorems. To cut a long story short: a vortex has uniform intensity (circulation) and it is either closed in a ring or originates from solid bodies at the boundary of the fluid domain (like wing tip vortices, or vortex sheets at the trailing edge of a wing) $\endgroup$
    – basics
    Oct 24, 2023 at 22:48
  • $\begingroup$ Hi but i thought invicid flow can no have circulation, since theres no shearing on elemental flow in the first place? $\endgroup$ Oct 31, 2023 at 9:55

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