Subject: Do fluids in a rotating sphere have viscous energy losses as t goes to inf?

This came up in a dinner discussion with my father. We're both decently sure
that a fluid encased in a rotating solid spherical shell will hit an
"equilibrium" of sorts, where everything moves at the same angular velocity
about an axis. I'm decently confindent that conservation of angular momentum
should apply, and after the sphere hits this equilibrium, it will keep rotating
without losses. The problem that I'm having is that this "equilibrium"
fundamentally involves a velocity gradient, and that might introduce viscous
losses in the rotating sphere.

This came up in a subset of discussion on the slowing of Earth's rotation. Is
that due to viscous losses in the core? I'm inclined to say "no", and that, in
fact, the sun is pulling the iron core against one side of the earth,
effectively grinding the system (otherwise in equilibrium) to a halt -- but that
this wouldn't happen if the sun's gravitational pull isn't there.

This also seems like a plausible explanation for why one side of the moon is
always facing the Earth -- if the Earth's pulling of the core slowed down the
rotation of the moon, then we'd expect it to only stabilize after the core and
the near portion of the moon's crust had the same angular velocity about the
Earth -- which means we'd always see the same portion of the moon's crust as it
rotated about the Earth.

Re: Do fluids in a rotating sphere have viscous energy losses as t goes to inf?