Existing studies of fish and bird locomotion typically assume the fins/wings oscillate sinusoidally. We explored what happens when the oscillations range from triangle waves to square waves. Triangle waves behave similarly to sine waves, but square waves show strong differences. Unlike sine waves, square waves result in a strong vortex pair shed every half-cycle, and thrust is up to four times higher, resulting in faster swimming speeds. (This work is from PI Quinn’s research prior to the SFS Lab and is archived here for reference.)
Authors: Tyler Van Buren, Daniel Floryan, Daniel Quinn, Alexander Smits
Abstract: 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.