Nonlinear dynamics of the wake of an oscillating cylinder

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Abstract
The wake of an oscillating cylinder at low Reynolds numbers is a nonlinear system in which a limit cycle due to natural vortex shedding is modulated, generating in phase space a flow on a torus. We experimentally show that the system displays Arnol’d tongues for rational frequency ratios, and approximates the devil’s staircase along the critical line. The ‘‘singularity spectrum’’ as well as spectral peaks at various Fibonacci sequences accompanying quasiperiodic transition to chaos shows that the system belongs to the same universality class as the sine circle map.