Effects of transverse curvature on oscillatory flow along a circular cylinder

Abstract

Oscillatory flows with zero mean velocity can be found in a variety of natural phenomena. The classic example of oscillatory flows in unbounded stagnant fluid is that over an infinite flat plate executing periodic sinusoidal motion along its plane. This was solved by Stokes and is often referred to in the literature as Stokes flow. Some characteristic features of this flow are that, although the flow oscillates at the same frequency as the plate, it lags behind the plate, and the phase lag is proportional to the distance from the plate. The layer of oscillatory flow also is referred to in the literature as 'Stokes layer'. In the present paper a general oscillatory Stokes flow including the transverse curvature effect is presented.