title: Oblique waves lift the flapping flag.
abstract: The flapping of the flag is a classical model problem for the understanding of fluid-structure interaction: How does the flat state lose stability? Why do the nonlinear effects induce hysteretic behavior? We show in this Letter that, in contrast with the commonly studied model, the full three-dimensional flag with gravity has no stationary state whose stability can be formally studied: The waves are oblique and must immediately be of large amplitude. The remarkable structure of these waves results from the interplay of weight, geometry, and aerodynamic forces. This pattern is a key element in the force balance which allows the flag to hold and fly in the wind: Large amplitude oblique waves are responsible for lift.
authors.affiliation: UPMC Univ Paris 06, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France. jerome.hoepffner@upmc.fr
authors.forename: Jérôme
authors.initials: J
authors.lastname: Hœpffner
authors.forename: Yoshitsugu
authors.initials: Y
authors.lastname: Naka