The onset of chaos in the wake of an oscillating cylinder: Experiment and the dynamics of the circle map

This paper deals with a comparison between experimental observations in low-Reynolds-number wake behind an oscillating cylinder and the universal properties of sine circle map. When the limit cycle due to the natural vortex shedding in the wake is modulated at a second frequency by oscillating the cylinder transversely, one obtain in phase space a flow on a two torus. The nonlinear interaction between the two oscillators in Arnol's tongues due to phase locking, the devil's staircase along the critical line, and a transition from order to chaos via the quasiperiodic route. The sine circle map describes these features adequately. A comparison between the experiment and the theory is made in terms of multifractal formalism and trajectory scaling function.