Fish Swimming and Bird/Insect Flight

This expository review is devoted to fish swimming and bird/insect flight. (a) The simple waving motion of an elongated flexible ribbon plate of constant width propagating a wave distally down the plate to swim forward in a fluid, initially at rest, is first considered to provide a fundamental concept on energy conservation. It is generalized to include variations in body width and thickness, with appended dorsal, ventral and caudal fins shedding vortices to closely simulate fish swimming, for which a nonlinear theory is presented for large-amplitude propulsion. (b) For bird flight, the pioneering studies on oscillatory rigid wings are discussed with delineating a fully nonlinear unsteady theory for a two-dimensional flexible wing with arbitrary variations in shape and trajectory to provide a comparative study with experiments. (c) For insect flight, recent advances are reviewed by items on aerodynamic theory and modeling, computational methods, and experiments, for forward and hovering flights with producing leading-edge vortex to yield unsteady high lift. (d) Prospects are explored on extracting prevailing intrinsic flow energy by fish and bird to enhance thrust for propulsion. (e) The mechanical and biological principles are drawn together for unified studies on the energetics in deriving metabolic power for animal locomotion, leading to the surprising discovery that the hydrodynamic viscous drag on swimming fish is largely associated with laminar boundary layers, thus drawing valid and sound evidences for a resounding resolution to the long-standing fish-swim paradox proclaimed by Gray (1936 , 1968 ).