  Manipulation ('shaking') of a rigid container filled with incompressible
liquid starting from stationary generally results in some displacement, or
mixing, of the liquid within it. If the liquid also has zero viscosity, a
'perfect', or Euler liquid, Kelvin's theorems dramatically simplify the flow
analysis. Response is instantaneous; stop the container and all liquid motion
stops. In fact an arbitrary manipulation can be considered as alternating
infinitesimal translations snd rotations of the container. Relative to the
container, the liquid is stationary during every translation. Infinitesimal
rotations (an infinitesimal vector along the rotation axis) resolve into three
orthogonal components in the container frame. Each generates its own
infinitesimal liquid displacement vector field. However these are rarely
tractable, and their combined consequences are obscure. Rather than a volume
flow, a surface flow in 3D is considerably easier, the liquid slipping freely
in a shell, sandwiched between two nested closed surfaces with constant
infinitesimal gap. The closedness avoids extra boundaries. The two
dimensionality admits a scalar streamfunction determined by the container
angular velocity vector. Manipulation of the container angular velocity at
will, leads (except for a sphere) to an infinitely rich variety of area
preserving re-configurations of the liquid. Even for a sphere, any chosen point
of the liquid can be moved, in the shell container frame, to any other point,
and one would expect the same in general. However, for torus with a small
enough hole (diameter<0.195 torus diameter), there exists a virtual wall, a
hypothetical axial cylinder intersecting the torus. No matter how the torus is
manipulated, liquid inside the cylinder stays inside; outside stays outside.
