On the instability of a spring-mounted circular cylinder in a viscous flowat low Reynolds numbers

The first instability of a spring-mounted, damped, rigid circular cylinder, immersed in a viscous flow and free to move in a direction orthogonal to t he unperturbed flow, is investigated by a global stability analysis. The fl ow is modelled by the full Navier-Stokes equations. For low ratios of the f luid density to the structure density, the von Karman mode is always the cr itical one and the critical Reynolds number, about 47, is nearly the same a s for a stationary cylinder. In this case, for low structural damping, two complex modes are active and chaos is possible near the bifurcation. For hi gher density ratios, the critical Reynolds number decreases to less than th e half the critical Reynolds number for a stationary structure. In this cas e, only a complex mode is active and chaotic behaviour does not seem to be possible near the bifurcation threshold. (C) 2000 Academic Press.