Nonsinusoidal gaits for unsteady propulsion

The impact of wave-form shape on the wake and propulsive performance of a pitching and heaving two-dimensional foil is explored experimentally. Jacobi elliptic functions are used to define wave-form shapes that are approximately triangular, sinusoidal, or square. The triangular-like and sinusoidal waves produce qualitatively similar wakes, with a typical reverse von Kármán vortex street structure leading to a jetlike wake in the mean. Square-like motions produce very different results, with a vortex pair shed every half cycle, leading to a mean wake with two distinct off-center jets, and a significant change in the thrust production, yielding up to four times more thrust for a given Strouhal number. Performance curves indicate that to swim most efficiently sinusoidal motions are best, whereas the square-like motions lead to higher speeds. A scaling analysis indicates that the peak lateral velocity appears to be the dominant parameter in characterizing the performance of the nonsinusoidal motions.