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Say you have a cylinder of perfectly rotating fluid, so that it's velocity field is:

F(x,y,z) = yi - xj

which has curl -2k

assuming there is 'infinite' fluid drag and you have an 'infinitely' light ball which you place into the fluid at any point (let's say it's centre).

then how fast would the ball be rotating?

In my head I equate this to having a ball cemented into a rotating cylinder of concrete (or simply an object sat ontop of a spinning disc) and it would have an angular velocity of -1rad/s.

but at the same time, it would seem to me that the spinning object should have an angular velocity equal to the curl of the fluid at that point, and of course -1 =/= -2