Qualitative features of high lift hovering dynamics and inertial manifolds

Abstract

Hovering aerodynamics, such as that practiced by dragonflys, hummingbirds, and certain other small insects, utilizes special patterns of vorticity to generate high lift flows. Such lift as we measure it computationally on the airfoil surface is in good agreement with downstream thrust measured in the physical laboratory. In this paper we examine the qualitative signatures of this dynamical system. A connection to the theory of inertial manifolds, more specifically the instance of time-dependent slow manifolds, is initiated. Additional interest attaches to the fact that in our compact computational domain, the forcing is on the boundary. Because of its highly oscillatory nature, in this dynamics one proceeds rapidly up the bifurcation ladder at relatively low Reynolds numbers. Thus, aside from its intrinsic interest, the hover model provides an attractive vehicle for a better understanding of dynamical system attractor dynamics and inertial manifold theory.