Weakly nonlinear analysis of the flutter motion of thin cylinders

Joël Tchoufag (1) , David Fabre (1) , Jacques Magnaudet (1)

1 IMFT - Institut de mécanique des fluides de Toulouse

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.

Mots clés: wake; Instability; Asymptotic expansion

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Joël Tchoufag, David Fabre, Jacques Magnaudet. Weakly nonlinear analysis of the flutter motion of thin cylinders. Ercoftac International Symposium on Unsteady separation in Fluid-Structure Interaction, Jun 2013, Mykonos, Greece. ⟨hal-00918002⟩