Flapping is an energy-demanding mode of fast animal locomotion that requires physiology, wing kinematics, and unsteady mechanics to work in unison. The trailing flow or wake is a signature of flapping mechanics, which makes it a popular candidate for visualization and analysis. While there are multiple ways to analyze wakes, we need a general framework to ensure utility of the analysis in bio-inspired flapping flight. In this article, we develop a theoretical framework to analyze the transport phenomena of wakes. To illustrate, we apply the theory to a two-dimensional modeled hovering flight comprising engineered rigid flapping plates, which vary in aspect ratio, wingbeat frequency, and the use of winglet. The results potentially explain certain observations in natural flight.
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