Quasiperiodicity and phase locking route to chaos in the 2D oscillatory flow around a circular cylinder

The two-dimensional oscillatory flow around a circular cylinder is analyzed by means of the numerical approach described in Justesen J. Fluid Mech. 222, 157 (1991). For a fixed value of the ratio between the Stokes viscous thickness and the radius of the cylinder section, when the Reynolds number assumes low values, the flow is periodic and symmetric with respect to an axis aligned with the flow direction and crossing the axis of the cylinder. An increase in the Reynolds number beyond a first critical value causes the flow to bifurcate: the velocity field loses its spatial symmetry even though it retains its time periodicity. When the Reynolds number is larger than a second critical value, a new frequency appears in the flow. This new frequency, which is much smaller than the frequency of the basic flow, increases for increasing values of the Reynolds number till a phase locking takes place. A further increase in the Reynolds number leads the flow to a chaotic status. The ''quasiperiodicity and phase locking'' route to chaos can be recognized.