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Fish typically swim by periodic bending of their bodies. Bending seems tofollow a universal rule; it occurs at about one-third from the posterior end ofthe fish body with a maximum bending angle of about $30^o$. However, thehydrodynamic mechanisms that shaped this convergent design and its potentialbenefit to fish in terms of swimming speed and efficiency are not wellunderstood. It is also unclear to what extent this bending is active or followspassively from the interaction of a flexible posterior with the fluidenvironment. Here, we use a self-propelled two-link model, with fluid-structureinteractions described in the context of the vortex sheet method, to analyzethe effects of both active and passive body bending on the swimmingperformance. We find that passive bending is more efficient but could reduceswimming speed compared to rigid flapping, but the addition of active bendingcould enhance both speed and efficiency. Importantly, we find that the phasedifference between the posterior and anterior sections of the body is animportant kinematic factor that influences performance, and that activeantiphase flexion, consistent with the passive flexion phase, cansimultaneously enhance speed and efficiency in a region of the design spacethat overlaps with biological observations. Our results are consistent with thehypothesis that fish that actively bend their bodies in a fashion that exploitspassive hydrodynamics can at once improve speed and efficiency.

Active tail flexion in concert with passive hydrodynamic forces improves swimming speed and efficiency