A numerical study of global frequency selection in the time-mean wake of a circular cylinder

A series of direct numerical simulations, both in two- and three-dimensions, of the flow past a circular cylinder for Reynolds numbers Re <= 600 has been conducted. From these simulations, the time-mean (and, for the three-dimensional simulations, the spanwise spatial-mean) flow has been calculated. A global linear stability analysis has been conducted on these mean flows, showing that the mean cylinder wake for Re <= 600 is marginally stable and the eigenfrequency of the leading global mode closely predicts the eventual saturated vortex shedding frequency. A local stability analysis has also been conducted. For this, a series of streamwise velocity profiles has been extracted from the mean wake and the stability of these profiles has been analysed using the Rayleigh stability equation. The real and imaginary instability frequencies gained from these profiles have then been used to find the global frequency selected by the flow using a saddle-point criterion. The results confirm the success of the saddle-point criterion when the mean flow is quasi-parallel in the vicinity of the saddle point; however, the limitations of the method when the mean flow exhibits higher curvature are also elucidated.