Energy dynamics in the helical wakes of flapping systems

Abstract

Hovering insects are adapted for high metabolism. Their physiology, morphology, and flight have similar scaling relations. However, there are differences in efficiency. For instance, bumblebees have superior efficiency over orchid bees. Here, we propose that unsteady aerodynamics can explain these differences. Inspired by helical wakes in the bumblebee flight, we study an unsteady viscous model to show that there is intermittently abundant energy in the wake which is available for extraction by flapping wings. We then investigate the transport phenomena in the model and identify the role of kinematic viscosity, nonlinearity, flow topology, and fluid dynamic current to justify the available energy. Wake energetics is applicable to other species such as hummingbirds whose responses rely on environmental conditions. The present work has implications in minimizing power consumption in bio-mimetic locomotion both in air and under water. Interdisciplinary applications include dynamic modeling in superfluid turbulence and magneto-fluid dynamic dynamo theory.