Oscillatory solution in rotating flow of a Johnson-Segalman fluid

A study is made of the flow engendered in a Johnson-Segalman, incompressible, rotating fluid bounded by a plate. Both the plate and the fluid are in a state of solid body rotation, and additionally a non-torsional oscillation of given frequency is superimposed on the plate for the generation of flow in the rotating system. The governing equations of motion for rotating flow of a Johnson-Segalman fluid are constructed. Periodic solutions are obtained for small Weissenberg number and we find that a Stokes-Ekman layer is formed on the plate for all frequencies except for the resonant frequency, which is twice the angular velocity of rotation. In the later case there is no oscillatory solution which satisfies the boundary conditions. The structure of the associated boundary layers for non-resonant case is determined.