Oscillatory Stokes flow in two dimensions (Q1804395)

Plane oscillatory Stokes flow has been discussed using circular harmonics. The solutions for (i) longitudinal oscillations of a circular cylinder in an unbounded flow, and (ii) oscillational shear flow past a circular cylinder have been obtained. The stream function in (i) can be interpreted as a combination of Stokeslet and potential doublet, and in (ii) can be identified as a combination of Stokeslet, Stokes dublet, and potential quadruplets. The flow field in the case (ii) can be compared with the flow due to a rigid plate moving in its own plane with sinusoidal variation of the velocity in a fluid otherwise at rest. Circle theorem for these flows has also been given.