Quasi-periodic cylinder wakes and the Ginzburg–Landau model

The time-periodic phenomena occurring at low Reynolds numbers (Re≤180) in the wake of a circular cylinder (finite-length section) are well modelled by a Ginzburg-Landau (GL) equation with zero boundary conditions (Albarede & Monkewitz). According to the GL model, the wake is mainly governed by a rescaled length, based on the aspect ratio and the Reynolds number. However, the determination of coefficients is not complete: we correct a former evaluation of the nonlinear Landau coefficient, we show difficulties in obtaining a consistent set of coefficients for different Reynolds numbers or end configurations, and we propose the use of an «influential» length. New two-point velocimetry results are presented: phase measurements show that a subtle property is shared by the three-dimensional wake and the GL model. Two time-quasi-periodic phenomena - the second mode observed for smaller aspect ratios, and the dislocated chevron observed for larger aspect ratios - are presented and precisely related to the GL model. Only the linear characteristics of the second mode are readily explained; its existence depends on the end conditions. Moreover, through a quasi-static variation of the length, the second mode evolves continuously to end cells (and vice versa). Observations of the dislocated chevron are recalled. A very similar instability is found on the chevron solution of the GL equation, when the model parameters (c 1 , c 2 ) move towards the phase diffusion unstable region. The early stages of this instability are qualitatively similar to the observed patterns