Connections between propulsive efficiency and wake structure via modal decomposition

A long-standing question in aquatic locomotion is whether the propulsive efficiency from a flapping or oscillating appendage can be determined from the downstream wake structure. We approach this problem by employing optimized Dynamic Mode Decomposition, a data-driven approach to better understand the dominant coherent structures in the wake region. We present Particle Image Velocimetry (PIV) results from a pitching and heaving NACA-0012 hydrofoil. Direct force measurements on the foil are also acquired to determine the peak propulsive efficiencies across different Strouhal numbers. We find that high efficiencies come from the reverse von Kárman 2S and 2P wakes. The resulting opt-DMD modes yield coherent Reynolds stresses that are characteristic of dynamic stall for Strouhal numbers, St ≥ 0.29, with beneficial stall effects contributing to the case of optimum efficiency. These results suggest that specific spatio-temporal modes obtained from opt-DMD or similar decomposition methods may show a better connection to the propulsive efficiency compared to the full wake structure.