Dynamic mode decomposition and stability analyses of oscillating foil wakes

Many swimming and flying animals make use of oscillating foils for efficient propulsion. Previous studies have shown that wake resonance plays an important role in determining hydrodynamic efficiency for oscillating foils. Optima in propulsive efficiency occur when the oscillation frequency coincides with the frequency corresponding to maximum spatial growth in the wake, as identified using linear stability analysis. Here, we combine linear stability analysis with Dynamic Mode Decomposition (DMD) to better understand the relationship between wake structure and propulsive efficiency. Experiments were performed using a NACA-0012 hydrofoil with heaving and pitching motions in a recirculating water channel. Direct measurements from a six-axis force sensor were used to determine thrust coefficients and Froude efficiencies for varying Strouhal number. 2D-2C Particle image velocimetry (PIV) measurements were carried out in the near-wake region of the oscillating foil to provide further insight into the wake structure. PIV time series data are used for DMD and the mean profiles are used for stability analyses. At peak Froude efficiencies, there is close correspondence between the DMD modes and stability analysis predictions. These observations are consistent with prior studies.