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I am studying Navier-Stokes and was trying to get a better intuition about the potential based formulation of the equations. I was working on a simple example. Imagine the fluid is moving at a constant velocity k in the \hat x direction then an expression for the vorticity giving this flow is ky\hat z. The flow is irrotational. Now imagine a closed loop somewhere in the +y half-plane. By stokes theorem we have a non-zero circulation. Am I doing something stupid or is this a degenerate case because to produce this flow we must have centers of rotation at plus and minus infinity in the y hat direction. I know the Helmholtz theorem requires source terms to vanish at infinity, but I don't recall a restriction on Stokes.
newbie

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Joined: Thu Nov 05, 2009 8:19 pm UTC

I may be misunderstanding you, but since the vorticity is the curl of the velocity field, I would say that your constant flow in a single direction will have 0 vorticity. When you say constant, do you mean time-invariant, or do you mean that the flow is the same everywhere? If the latter, it would result in 0 vorticity because dk/dy = 0.

cpt

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