Stability properties of forced wakes

Thiria, Goujon-Durand & Wesfreid (J. Fluid Mech. vol. 560, 2006, p. 123), it was shown that vortex shedding from a rotationally oscillating cylinder at moderate Reynolds number can be characterized by the spatial coexistence of two distinct patterns, one of which is related to the forcing frequency in the near wake and the other to a frequency close to the natural one for the unforced case downstream of this locked region. The existence and the modification of these wake characteristics were found to be strongly affected by the frequency and the amplitude of the cylinder oscillation. In this paper, a linear stability analysis of these forced regimes is performed, and shows that the stability characteristics of such flows are governed by a strong mean flow correction which is a function of the oscillation parameters. We also present experiments on the spatial properties of the global mode and on the selection of the vortex shedding frequency as a function of the forcing conditions for Re = 150. Finally, we elucidate a diagram of locked and non-locked states, for a large range of frequencies and amplitudes of the oscillation.