Three-dimensional Instability in the Wake of a Pitching Foil

In this paper, we investigate the three-dimensional transition of a propulsive wake, which is generated by a pitching foil, mimicking the caudal fin of a fish. We note that a fish fin is usually of very short aspect ratio, here we assume an infinite span, aiming to reveal the fundamental physical mechanisms. For the base flow, three sequential wake structures are identified as we increase the pitching amplitude, while fixing the pitching frequency. They are Bénard-von Kármán (BvK) vortex street, reverse BvK vortex street and deflected wake, respectively. Through Floquet analysis, we observe an unstable mode at the wavelength λz = 0.21, while another mode also becomes critical with a longer wavelength at λz = 1.05. However, we point out that the long wavelength mode can not be observed physically, because its growth rate is always less than the short wavelength mode. The long wavelength mode resembles that of the so-called mode A in the drag wake of a fixed bluff body. While the short wavelength mode repeats the perturbation field every second cycle of the base flow.