Dynamical features of the wake behind a pitching foil

As an extension of the previous study on the three-dimensional transition of the wake behind a pitching foil [Deng and Caulfield, Phys. Rev. E 91, 043017 (2015)], this investigation draws a comprehensive map on the pitching frequency-amplitude phase space. First, by fixing the Reynolds number at Re = 1700 and varying the pitching frequency and amplitude, we identify three key dynamical features of the wake: first, the transition from Benard-von Karman (BvK) vortex streets to reverse BvK vortex streets, and second, the symmetry breaking of this reverse BvK wake leading to a deflected wake, and a further transition from two-dimensional (2D) wakes to three-dimensional (3D) wakes. The transition boundary between the 2D and 3D wakes lies top right of the wake deflection boundary, implying a correlation between the wake deflection and the 2D to 3D wake transition, confirming that this transition occurs after the wake deflection. This paper supports the previous extensive numerical studies under two-dimensional assumption at low Reynolds number, since it is indeed two dimensional except for the cases at very high pitching frequencies or large amplitudes. Furthermore, by three-dimensional direct numerical simulations (DNSs), we confirm the previous statement about the physical realizability of the short wavelength mode at beta = 30 (or lambda(z) = 0.21) for Re = 1500. By comparing the three-dimensional vortical structures by DNSs with that from the reconstruction of Floquet modes, we find a good consistency between them, both exhibiting clear streamwise structures in the wake.