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I am a mathematician that is interested in how physicists justify the creation and persistence of vortices (such as bathtub vortex or tornados) from Navier Stokes.

The explicit solutions I have come from relatively contrived examples such as a perfectly symmetrical container spinning evenly. I am much more interested in an argument that would show that a vortex is likely to form under certain conditions (such as a drain being pulled). For example, a qualitative argument based on Helmholtz's theorems or Kelvin's circulation theorem would be very interesting to me.

I would appreciate any relevant resources.

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