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Does a fluid with velocity $q =\left (z-\frac{2x}{r},2y-3z-\frac{2y}{r},x-3y-\frac{2z}{r}\right)$ posses vorticity? What is the circulation in the circle $x^2+y^2 = 9$, $z =0$ ?

where $r^2=(x^2 + y^2 + z^2)$

PS: This question has been asked already but I wanted to know the concept behind it. I am getting Vortex vector as zero vector. Does vorticity means vortex vector is zero ?

And what is the difference in circulation and vorticity ? Shouldn't the circulation be also zero here as vortex vector is zero ?

user1611542
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  • Does this help? https://en.m.wikipedia.org/wiki/Circulation_%28fluid_dynamics%29?wprov=sfla1 – Eddy Oct 20 '17 at 18:05
  • I got the vorticity part. But not the circulation one. According to the page vorticity is circulation per unit area. So circulation should also be zero ? – user1611542 Oct 20 '17 at 18:53
  • Circulation is the integral of vorticity across a surface, so if the vorticity is zero, the circular is zero. – Eddy Oct 20 '17 at 18:54
  • See the section "Relation to vorticity" in the link – Eddy Oct 20 '17 at 18:57

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