Dynamics of tethered membranes in inviscid flow

We study the dynamics of membranes (with stretching stiffness but zero bending stiffness) that shed vortex wakes in inviscid flows. Previous studies have focused on membranes with fixed ends, where only static deflection occurs. Here we consider instead membranes held by tethers with hinged ends, and find that a variety of unsteady large-amplitude motions, both periodic and chaotic, may occur. We characterize the dynamics over ranges of the key parameters: membrane mass density, stretching stiffness, pretension, and tether length. We find the region of instability and the small-amplitude behavior in a linearized model by solving a nonlinear eigenvalue problem. We also derive asymptotic scaling laws by considering a simplified model: an infinite periodic membrane. We find qualitative similarities among all three models in terms of the oscillation frequencies and membrane shapes at small and large values of the parameters.