Mode Transition and Symmetry-Breaking in the Wake of a Flapping Foil

A numerical model for two-dimensional flows around a pitching foil in a viscous flow is presented. The model is numerically solved using the immersed boundary method and used to investigate the flow patterns of the foil pitching sinusoidally over a range of frequencies and amplitudes. A transition from the Karman vortex streets to the reverse Karman vortex streets are found, as the amplitudes of pitching motions increase. In the transition, the vortex streets undergo symmetry-breaking to the central lines of vortex streets. Those observations are in agreement with the previous experiment (Phys. Rev. E. 77 016308 2008). Furthermore, we examine the wake of the foils pitching with different frequencies. The transition from the Karman vortex streets to the reverse Karman vortex streets is also observed. An explanation is presented to the mechanism of the transition.