Stability of the vortex motion in oscillating flow.

Abstract

Previous experimental investigations have shown that the characteristics of flow about a circular cylinder immersed in a time-dependent flow exhibit cycle-to-cycle variations. These variations have been attributed to the variations in the spanwise coherence, aspect ratio, nonuniformity of the flow, and random disturbances in the ambient flow. A theoretical investigation was undertaken to examine the stability of the flow characteristics in terms of the initial state of the vortices. An idealized model has been devised and the position of the vortex was varied systematically. The results have shown that finite-precision information about the characteristics of the flow does not lead to finite-precision information at a later stage. In fact the advection of the vortices can give rise to chaotic behavior in the calculated lift and drag forces and in the velocity field. It is concluded that the cycle-to-cycle variations are not entirely due to lack of spanwise coherence and that they are mostly a consequence of the chaotic motion which can result from the advection of the vortices in a time-dependent flow.