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

Swimming fish have a universal rule in bending their body during swimming; it occurs at about one-third from the tail of fish with a maximum bending angle of about 30o. However, the hydrodynamic mechanisms that shaped this convergent design and its potential benefit to fish in terms of swimming speed and efficiency are not well understood. It is also unclear to what extent this bending is active or passively follows the interaction of a flexible posterior with the fluid. Here, we analyze the swimming performance of a self-propelled two-link plate with active and passive posterior end in the context of the vortex sheet method. Passive bending is more efficient but slower, but active bending can enhance both speed and efficiency. Importantly, we find that the phase difference between the posterior and anterior of the body is an important kinematic factor that influences performance. Active antiphase flexion, consistent with the passive flexion phase, can simultaneously enhance speed and efficiency in a region within the design space that overlaps with biological observations. Our results shows that fish that actively bend their bodies could exploits passive hydrodynamics can at once improve speed and efficiency.