Reduced-order modeling of propulsive vortex shedding from a free pitching hydrofoil with an internal rotor

The efficient development of control strategies for biomimetic aquatic vehicles that exploit vortex shedding for propulsion requires mathematical models that are sufficiently rich to capture the necessary hydrodynamic phenomena while remaining computationally tractable, and if possible while offering some interface to analytical (in addition to computational) tools. In a sequence of recent papers, the authors have detailed an approach to modeling such systems that exploits certain idealizations to realize equations of motion that accommodate the formalism of geometric mechanics on manifolds, and have demonstrated the relevance of resulting models to actual robotic systems. In the present paper, we describe an amended approach to modeling propulsive vortex shedding in the plane that retains critical features of previous models while providing a significant decrease in model dimension. We illustrate our updated approach by simulating the dynamics of a prototypical fishlike swimmer comprising a free rigid hydrofoil that can be induced to pivot about a body-fixed point through the oscillation of an internal rotor, shedding propulsive vorticity from its trailing edge.