A Universal Vortex-Formation Law for Insect Hovering

Abstract

Flapping insect wings generate leading-edge vortices (LEVs) that produce much of the lift required for hovering, yet the frequency governing their formation has not been connected to classical vortex shedding. Roshko scaling for bluff-body wakes, together with the Sigurdson extension to wall-bounded separated flows, identifies a universal vortex-formation Strouhal-number range of approximately 0.15 to 0.17. Here we show that this same range governs LEV formation on both stationary wings and hovering insect wings. We first develop an approximate scaling for stationary flat-plate wings in which discrete LEVs are generated by periodic leading-edge perturbations, and show that maximum lift consistently occurs within the universal Strouhal range. In hovering insects, one LEV forms during each translational half-stroke, allowing the same framework to be applied to published flight data. Despite large differences in morphology, kinematics and Reynolds number, the insect data recover the same Strouhal range. These results reveal a common vortex-formation timescale linking classical separated flows, artificially generated LEVs and the natural LEVs that sustain insect hovering.