Bistable states in the wake of a wavy cylinder

Wavy cylinders have been recognized as a type of effective flow control device in previous studies. In this paper, we investigate the wake dynamics of an optimally designed wavy cylinder that completely suppresses the Karman vortex shedding. Such a wavy cylinder is forced to oscillate with a sinusoidal motion in the crossflow direction. Examination of the lift force spectrum reveals that for a fixed forcing amplitude, a critical forcing frequency exists, below which the flow control effectiveness of the wavy cylinder is retained and beyond which the inherent vortex shedding resurrects. The resurrected unsteady vortex shedding can persist even without sustained forcing. This indicates that in addition to the steady state developed from uniform initial condition, an oscillatory state exists in the wake of a wavy cylinder if the initial state is sufficiently perturbed. The newly revealed unsteady flow features comparable hydrodynamic performance with the benchmark two-dimensional cylinder. The discovery of the bistable states calls for re-examination of the flow control effectiveness of the wavy cylinder in more complicated inflow conditions.