Constraining optimum swimming strategies in plesiosaurs: The effect of amplitude ratio on tandem pitching foils

Identical tandem flippers of plesiosaurs, which are unique among all animals, have been a source of debate regarding the role of hind flippers in their locomotion. Here, inspired by the kinematics of plesiosaur flippers, the effect of the amplitude ratio on the propulsive performance of in-line tandem pitching foils is investigated through a series of particle image velocimetry experiments. Three leader-to-follower amplitude ratios are considered for the foils pitching over a range of $0–2π$ phase difference. For the first time, it is shown that the amplitude ratio can significantly affect the performance of the hind foil at spacing larger than one chord length. It is found that the thrust generation of the hind foil at the optimum phase difference augments by 130% when it is pitching at the twice angular amplitude of the upstream foil. Although the total performance of the rear-biased and equal amplitude models reaches similar values, thrust production of the hind foil in the equal amplitude model increases only by 23%. By contrast, the performance of the forward-biased model decreases drastically for all phase differences due to the destructive wake–foil interaction of the hind foil. Studying the instantaneous wake–foil interactions, it is found that high thrust generation is associated with the formation of a vortex pair on the suction side of the hind foil, which causes stronger trailing edge vortices to shed with a greater total wake spacing. Finally, through scaling analysis, high-thrust configurations of tandem models are ranked based on the total efficiency of the system.