Hydrodynamics of flapping foils undergoing irregular motion with application to wave-assisted propulsion

Flapping foils are widely studied as bioinspired propulsors, yet most investigations have focused on regular, sinusoidal kinematics. In realistic environments, however, irregular motions arise naturally due to environmental disturbances, fluid–structure interactions and control inputs, but their hydrodynamic consequences remain largely unexplored. One system where response to irregular forcing is particularly relevant is wave-assisted propulsion (WAP) systems where free-to-pitch submerged foils generate thrust due to wave-induced heaving. We employ time-accurate flow simulations of elliptic WAP foils subjected to irregular waves at three different sea-states to gain insights into this system. Our results demonstrate that irregular heaving and pitching can generate greater mean thrust than energetically equivalent sinusoidal heaving. Moreover, a spring-based pitch-limiting mechanism yields higher thrust than an angle-limiter under the same conditions. By leveraging a previously developed leading-edge vortex model, we uncover the mechanisms driving this thrust enhancement and highlight the critical interactions between unsteady flow structures and foil dynamics. These findings provide new insights into flapping-foil propulsion in irregular environments and have direct implications for the design and optimization of WAP systems.