Secondary Flow Induced by a Circular Cylinder Oscillating in Two Directions

This paper deals theoretically with the two-dimensional flow induced by a circular cylinder translationally oscillating in an unbounded visous fluid otherwise at rest. The oscillation is composed of a harmonic oscillation with a frequency normal to the axis of the cylinder and another harmonic one with double frequency perpendicular to the former and the axis. Steady secondary flow is studied in detail by the method of successive approximations. It is shown that a uniform flow is induced at infinity. The direction of the uniform flow can change according as a Reynolds number. This is qualitatively similar to the result of the available experimental result on the flow around a circular cylinder which performs an eccentric relational oscillation. The direction depends ends also on the type of the motion of the cylinder, which traces, in general, a Lissajous's figure.