Multiple Stable/Unstable Equilibria of a Cylinder in the Wake of an Upstream Cylinder

Abstract

The static equilibrium position and its associated dynamic stability of a cylinder situated in the wake of an upstream cylinder is investigated in this paper. Both the upstream and downstream cylinders are elastically mounted on springs to allow for streamwise and transverse displacements. Due to the wake effect the downstream cylinder is subject to a lift force as well as a drag. It is shown that under certain flow conditions there exist multiple stable and unstable equilibria for the downstream cylinder. There also exist a critical flow velocity and once this velocity is exceeded no equilibrium positions of the downstream cylinder can be found, which suggests a likely occurrence of clashing between the two cylinders.