An incompressible homogeneous fluid is contained within a circular cylindrical can and the whole system is rotating uniformly about the axis of the can. In addition the boundary performs small amplitude torsional oscillations about the axis of the cylinder; the oscillations of the flat and curved portions of the cylinder may differ in amplitude and frequency. It is shown that either oscillatory Stewarteon layers or a Stokes layer is formed on the curved portion of the cylinder depending upon the magnitude of the imposed oscillation on that boundary. In addition it is shown that, except when resonant oscillations are present on the flat surfaces of the can, the effects of the curved side wall are restricted to the immediate vicinity of this boundary and elsewhere in the fluid the solutions agree with the solutions obtained by Jaoobs (1) for the laterally unbounded problem. However when the flat surfaces of the can oscillate at the resonant frequency, the presence of the curved side wall introduces a length scale whioh enables an additional boundary layer to be formed on the flat surfaces of the can. Hence a new solution emerges which differs from the solution of the laterally unbounded problem everywhere in the fluid.
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