Weakly nonlinear analysis of the flutter motion of thin cylinders

Abstract

The nature overflows with examples which prove that buoyancy-driven objects in a viscous medium can result in diverse and exotic trajectories. Among them is found the so-called Zig-Zag (ZZ)path or flutter which we investigate in the present work. The configuration is that of a thin cylinder initially rising/falling vertically in an unbounded fluid otherwise at rest. The problem is parametrized by the aspect ratio (diameter to thickness) X, the moment of inertia I* and Archimedes number (gravitational-velocity-based Reynolds) Ar. For small I*, past studies have reported asupercritical transition from the vertical to the ZZ path at a critical Arc. We show by means of linear and weakly nonlinear analyses that the observed flutter results from the nonlinear saturation of an unstable global mode of the coupled fluid+disk problem.