Optimum gaits and synchronization of a self-propelled undulatory motion in fish pair and fish arrays.

The bio-locomotion of self-propelled underwater undulatory swimmers is investigated and optimized using a high-fidelity computational framework. The kinematic gaits and the phase lag between two side by side self-propelled swimmers are optimized for swimming efficiency using a global surrogate based optimization algorithm. Hydrodynamic trends governing optimal and sub-optimal swimming behaviour are investigated using modes which arise from the optimization procedure. Additionally, we vary the distance between the two swimmers to investigate separation effects on kinematics in fish pair swimming. Our results confirm the superiority of anti-phase lag between swimming pair and provide a measure of sensitivity of swimming efficiency to phase lag. Moreover, the optimal kinematic gait is shown to be dependent on the separation distance up to a certain point, D*, where the optimal kinematic gaits approach the single swimmer limit. Finally, we extend our analysis to the case of optimal swimming efficiency for an infinite array of side-by-side swimmers.