Summary: The presented numerical simulations focus on the strong non-linear effects at the onset of three-dimensionality in the circular cylinder wake. The obtained numerical results shed light on the link between the linear theory and experimental observations. The latter are represented mainly by the Williamson’s Strouhal vs. Reynolds number experimental curve presenting a double discontinuity at the onset of three-dimensionality. In this paper, we show that the subcritical nature of the secondary bifurcation triggering the three-dimensionality considerably weakens the relevance of linear predictions. We first investigate the bi-stability interval of the subcritical bifurcation as a function of the spanwise periodicity of simulations. This allows us to define a non-linear marginal stability curve and to show that it predicts no preferred wavelength. The large spanwise scales and their effect on the simulated flow are then investigated in simulations with a spanwise periodicity of 31.4d and run for subcritical Reynolds numbers \(Re = 185\), \(170\), and \(160\). It is shown that the non-linear state is chaotic and that the bi-stability interval in which it co-exists with the 2D parallel vortex shedding extends at least from \(Re=170\) to the linear secondary instability threshold lying between \(Re=188\) and \(Re=189\). Strouhal numbers obtained in simulations with a spanwise period close to 4d (linear preferred wavelength) tend to overestimate the Strouhal number drop. Simulations with a large spanwise period tend to put the Strouhal number closer to experimental values. Below the bi-stability interval, at \(Re=160\), the wake is observed to settle from the chaotic state to oblique vortex shedding.{
©2011 American Institute of Physics}