Secondary Flow Induced by an Unharmonically Oscillating Circular Cylinder

Abstract

This paper deals theoretically with the two-dimensional flow driven by a circular cylinder which performs unharmonically translational oscillation in an unbounded viscous incompressible fluid otherwise at rest. Slow steady secondary flow occurs outside the oscillatory boundary layer around the cylinder, provided that the non-dimensional amplitude of the oscillation ε and the boundary layer thickness are both extremely small. It is found that induced steady flow of O(ε) is symmetric with respect to the direction of the oscillation and vanishes at infinity; however, in O(ε²) asymmetric steady streaming is induced in the main field and remains at infinity as a uniform flow in the direction of oscillation, due to the effect of the asymmetry in the motion of the circular cylinder.