Numerical study on the hydrodynamics of porpoising behavior in dolphins

Abstract This paper employs numerical simulation to study the hydrodynamics of porpoising behavior in dolphins. The virtual swimmer is a three-dimensional dolphin-like body with prescribed kinematics. A four-stage model of this behavior is proposed, including underwater acceleration, upward leap, air glide and downward dive. When the dolphin goes through these four stages, the time history of its displacement, velocity, force and energy could be solved to elucidate the rules. By varying oscillating frequency f and escape angle α, various behaviors of the swimmer are simulated to obtain their porpoising performance, which are evaluated by maximum leap height Hmax, maximum leap distance Dmax and leap efficiency η. The results show that both Hmax and Dmax are increasing functions of f, but their trend with α is not monotonic. For peak Hmax generation, α occurs at 90°, while for peak Dmax, α is ranging from 45° to 60° and nears 50°. As for efficiency, η increases slowly with the increase of α, and first increases and then decreases with the increase of f at a critical value between 7 Hz and 8 Hz. The findings may provide an important hydrodynamics basis for the biomimetic vehicle designs that mimic the porpoising motion of dolphins.