'Universal' dynamics in the wake of an oscillating cylinder at low Reynolds numbers

Authors present experimental observations in the wake of an oscillating circular cylinder at low Reynolds numbers. The fluid system is one in which a limit cycle (corresponding to the natural vortex shedding) is modulated at a second frequency (due to the cylinder oscillation) generating in phase space a flow on a torus. At rational values of the frequency ratio, the system displays Arnold tongues due to phase locking, leading to a behavior approximating the devil's staircase along the critical line. Associated with quasiperiodic transition at the golden mean frequency ratio, spectral peaks appear at various Fibonacci sequences. These as well as the 'singularity spectrum' of the Poincare section of the attractor at the critical golden mean point are largely similar to the universal characteristics of the sine circle map, the observed departures being within experimental uncertainties.