Freedom of Science

Water inside a rotating sphere:

I assume that the spiral shape arises because the bottom of the vortex touches the sphere?

Here’s a simplified geometry of the same phenomenon:

This is figure 11.7: Shape of liquid surface in a rotating bucket, in Equilibrium statistical physics by Michael Plischke and Birger Bergersen. They reason that “in a normal fluid, rotating uniformly, the shape of the upper surface is determined by a balance between the centripetal and gravitational forces giving

But I believe that the shape can be investigated geometrically without considering gravity or pressure. I don’t know if this is true. I have a sketch here that was inspired by Doug’s comment at Mass.

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