Dynamic responses of a two-dimensional flapping foil motion

The investigation of a flapping foil, which is used as a basic mode of the flapping-based locomotion in insects, birds, and fish, is performed by solving the Navier-Stokes equations numerically. In this Brief Communication we provide insight into the understanding of dynamics of a flapping foil. A critical flapping Reynolds number based on the flapping frequency and amplitude, above which a forward flapping movement occurs, is predicted. The dynamics of the flapping foil are analyzed in two dynamic responses, i.e., an oscillatory movement and a steady movement, which depend on the density ratio between the foil and the surrounded fluid. The steady movement response is related to the forward flapping motion. The Strouhal number that governs a vortex shedding for the forward flapping foil is calculated and lies in the range where flying and swimming animals will be likely to tune for high propulsive efficiency.