Generalization of vortex formation time for animal flight

Vortex formation is significantly related to propulsion of biological organisms. Specifically, vortices play an important role when aerial organisms generate lift and thrust. The dimensionless vortex formation time of an airborne biological system depends on wing kinematics and morphology, as well as its flight conditions. To generalize the dimensionless vortex formation time, we conducted meta-analysis of 11 literature with complete flight kinematics information of a wide range of biological flyers with Reynolds numbers ranging from $O(10^2)$ to $O(10^5)$. It is found that vortex formation time falls in a narrow range when defined as a function of velocity scale associated with vorticity generation, length scale that limits the growth of the vortex, and the time duration of the vorticity injection. Such findings suggest that instead of the optimization of frequency-based paramters, biological flyers optimize their wing kinematics for each cycle.