Nonlinear Dynamics Analysis of a Flapping Filament in a Flowing Soap Film*

In this study we investigate the nonlinear dynamics of the flapping regime of a filament placed in a two-dimensional soap film flow for different filament lengths and flow speeds. The results show that the onset of flapping at very high Reynolds numbers is quasi-periodic, with the main flapping amplitude and frequency modulated by low-amplitude, low-frequency oscillation. At higher flow velocities, chaotic oscillation is observed. The transition to chaos occurs via the quasi-periodic route to chaos. A new bistability phenomenon is discovered in which the system alternates between the stretched-straight and oscillatory states, and is referred in this study to as ``switching oscillation.'' Unlike some previously reported forms of bistability, in this case the system alternates between the two states continuously, without any external perturbation.