Free Vortex Flow: Vorticity & Streamlines at Eye of Vortex

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SUMMARY

The discussion centers on the characteristics of free vortex flow, specifically addressing the behavior of velocity components at the eye of the vortex. In free vortex flow, only the tangential component of the velocity vector is present, while the radial component is zero. At the eye of the vortex, which is identified as a singularity, the concept of tangential velocity becomes undefined, leading to unique implications for vorticity and streamlines in this region.

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TL;DR
Non-trivial component of velocity vector is tangential?
In free vortex what does it mean " non-trivial component of velocity vector is tangential"? I know only the tangential component of velocity exists in free vortex flow, so what happens at the eye of the vortex ( what happens to vorticity and streamlines to be specific)?
 
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The eye of a vortex is a singularity, so the concept of tangential velocity breaks down entirely.
 
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