The Effect of Aspect Ratio and Angle of Attack on the Transition Regions of the Inverted Flag Instability

The fluttering flag instability has been thoroughly studied through experimental, computational and theoretical means. However, each of these studies only considers the boundary conditions where a flagpole or other tethering mechanism precedes the plate in the fluid flow. Under the inverse condition, where the so-called flag is fixed by its downstream edge in the fluid flow, three regions of behavior exist: straight, flapping, and bent back. This paper expands on these findings by closely examining the transition regions between straight and flapping and flapping and bent back. The onset mechanism of the instability and the terminating mechanism are shown to be dependent on different factors. The region of flapping occurs within a narrow range of non-dimensional bending stiffness, with the region boundaries depending on the aspect ratio and angle of attack of the plate.