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potential flow vs. Euler flow

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Old   July 11, 2006, 07:34
Default Re: potential flow vs. Euler flow
  #21
Tom
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What Andrin is getting at is that in 2D vortex lines must be either open, closed loops or end on a boundary (essentially the Poincare-Bendixon theorem for planar odes). In 3D you have the possibility that a vortex line can infinitely wrap around itself as well; e.g. the vortex lines could be quasi-periodic or even chaotic - the vortex line equations are a system of odes in 3D and so behaviour like that of the Lorenz attractor cannot be ruled out.
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Old   July 11, 2006, 07:48
Default Re: potential flow vs. Euler flow
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Gerrit
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Thanks! (Again)
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Old   July 11, 2006, 18:49
Default Re: potential flow vs. Euler flow
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Adrin Gharakhani
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>> think that's the Helmholz theorem, saying that a vortex should always be a closed curve

Tom already stated almost precisely what I meant and had in mind. I will only add here vortex lines in viscous flows, which, again, don't necessarily form closed loops.

The particular Helmoltz Theorem is just an expression of the solenoidality of the vorticity field (kinematics, nothing more). To this end, it is true that all closed loops will satisfy this condition, but a solenoidal field does not have to be in the form of a closed loop, as Tom has nicely pointed out. (it's a matter of necessary vs. sufficient condition)

adrin

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Old   July 21, 2006, 07:40
Default Re: potential flow vs. Euler flow
  #24
mar
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Only a comment: I don't agree with the one who said that the circulation is inserted in the aerodynamic field by the "numerical dissipation". The explanation in fact is in the boundary condition you are applying at the edge. In numerics it's a common practice to have a the trailing edge two points which are topologically disconnected but that have the same coordinates (geometrically coincident). To solve the problem of the uniqueness of the solution at the trailing edge what it's actually done is to calculate the aerodynamic field at one of this point (starting from the interior points) and to assign this field at both points. In this way the Kutta condition is "naturally" imposed; you have not to calculate in an explicit way the circulation as must be done in potential flows...

I hope I've been clearer this time
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