The most beautiful rotating fluid is 2900 km under our feet; that's the liquid core of the Earth. It is the source of the geodynamo: as it is made of almost pure liquid iron,  the liquid core of the Earth can generate magnetic fields some of which is detectable where we live.
    The liquid core of the Earth is a spherical shell 2200 km thick which is limited on its inner part by the inner core which is though to be solid iron. Liquid iron is like mercury not very viscous and because velocities are not very large (1mm/s) the Coriolis force dominates the dynamics of the liquid core. Liquid iron is also not much compressible and the density of the fluid therefore does not vary very much within the core. We thus have at hands an almost canonical example of a rotating fluid contained in a spherical shell ! Since some of its motion are detected we may learn something on the physics of this part of the Earth: you may have a look to:
 

• Rieutord M. (1995), "Inertial modes in the liquid core of the Earth", Phys. Earth Plan. Int. vol. 90, pp.~41--46.
• Rieutord M. (2000), "A note on inertial modes in the core of the Earth", Phys. Earth Plan. Int., vol. 117, pp. 63-70.
• Rieutord M. (2002), "Slichter modes of the Earth revisited", Phys. Earth Plan. Int., vol. 131, pp. 269-78.