The Hovering Hat

Birds and insects often flap their wings to hover and fly. Interestingly, recent experiments have shown that non-flapping rigid objects are also capable of stably hovering in an oscillatory background flow, given they possess particular geometric asymmetry in the vertical direction. The up-down asymmetry creates downwash vortex shedding and thus generates lift against gravity. Here, we use a two-dimensional vortex sheet model to study the motion of an inverted V-shaped object, moving passively in an oscillatory flow. We found that, depending on the fluid oscillation frequency, the hat descends, hovers or ascends. We also found an optimal opening angle of the hat for hovering that requires minimal energy from the background flow. We conclude by showing the passive stability of the hat and the role of the hydrodynamic forces and moments in preventing it from tipping over.