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.