This is the last problem in the aerodynamics book by Scorer (1958). I am failing to see how the tea in the cup can be stirred, simply by the circular motion of the lady around an axis external to both the woman and the cup.

Can anyone offer any insights or perspective that might help me understand the problem better?

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  • $\begingroup$ What do you feel when you go down a helical slide or around a roundabout? $\endgroup$ – lux Nov 23 '19 at 15:36
  • $\begingroup$ @lux - centrifugal forces? but that would only affect the pressure distribution (maybe? :P) $\endgroup$ – nikhil Nov 23 '19 at 16:41
  • $\begingroup$ Would that provide different forces and movement for different constituents in the tea? $\endgroup$ – lux Nov 23 '19 at 17:57
  • $\begingroup$ @nikhil What would happen if you went down the winding stair holding an almost frictionless bearing (assuming the axis of the bearing is parallel to the axis of the winding stair)? $\endgroup$ – 2b-t Nov 23 '19 at 18:44
  • $\begingroup$ Make a simple experiment. Pour tea into a cup so that there are tea leaves. Hold the cup horizontally on your outstretched arm. Spin around your axis. You will see that the tea leaves are moving, spinning in the direction opposite to your rotation. Stop abruptly. Now the tea leaves move following your rotation. Explain the movement in the cup:) $\endgroup$ – Alex Trounev Nov 25 '19 at 22:04

When a person holding the cup of tea is descending on a spiral staircase, they're moving downwards and are rotating about its axis. Linear motion is irrelevant in this case, only the rotational part matters. And exactly the same thing happens as if you were to rotate the cup: it rotates relative to fluid inside. As boundary layer of the fluid that contacts the cup is dragged along with the cup, inner parts of the fluid are still stationary due to inertia, and this velocity gradient creates turbulence that can mix fluid inside if it has enough intensity.

In practice, however, I think it'd take quite a long staircase to mix a cup of coffee properly.


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