  We investigate the hovering dynamics of rigid bodies with up-down asymmetry
placed in oscillating background flows. Recent experiments on inanimate
pyramid-shaped objects in oscillating flows with zero mean component
demonstrate that the resulting aerodynamic forces are sufficient to keep the
object aloft. The mechanisms responsible for this lift production are
fundamentally unsteady and depend on the shed vorticity. Here, we consider a
model system of a two-dimensional flyer and compute the unsteady, two-way
coupling between the flyer and the surrounding fluid in the context of the
vortex sheet model. We examine in detail the flow properties (frequency and
speed) required for hovering and their dependence on the flyer's
characteristics (mass and geometry). We find that the aerodynamic effort
required to hover is an intrinsic property of the flyer itself: a given flyer
requires a constant amount of effort to hover, irrespective of the frequency
and speed of the oscillating flow. This physical insight will potentially have
significant implications on the design of unmanned air vehicles as well as on
understanding active hovering of live organisms that can manipulate their
flapping motion to favor a larger oscillation amplitude or frequency.
