Evidence of holes in the Arnold tongues of flow past two oscillating cylinders

The wake of two oscillating cylinders in a tandem arrangement is a nonlinear system that displays Arnold tongues. We show by numerical simulations that their geometry depends on the phase difference theta between the two oscillating cylinders. At theta = 0 there may be holes inside these intraresonance regions unlike the solid Arnold tongues encountered in single-cylinder oscillations. This implies that, surprisingly, self-excitation of the system may be suppressed inside these holes, at conditions close to its natural frequency.