Undulatory hydrodynamics of tapered elastic plates in viscous fluid

The hydrodynamic performance of oscillating elastic plates with tapered and uniform thickness in an incompressible Newtonian fluid at varying Reynolds numbers is investigated numerically using a fully coupled fluid–structure interaction computational model. By leveraging the acoustic black hole effect, tapered plates can generate bending patterns that vary from standing wave to travelling wave oscillations, whereas plates with uniform thickness are limited to standing wave oscillations. Simulations reveal that although both standing and traveling wave oscillation modes can produce high thrust, travelling waves achieve significantly higher hydrodynamic efficiency, and this advantage is more pronounced at higher Reynolds numbers. Furthermore, regardless of the oscillation mode, tapering leads to greater hydrodynamic performance. The enhanced hydrodynamic efficiency of travelling wave propulsion is associated with the reduced amount of vorticity generated by tapered plates, while maintaining high tip displacements. The results have implications for the development of highly efficient biomimetic robotic swimmers, and more generally, the better understanding of the undulatory aquatic locomotion.