QUASI-PERIODIC CYLINDER WAKES AND THE GINZBURG-LANDAU MODEL

The time-periodic phenomena occurring at low Reynolds numbers (Re less than or similar to 180) in the wake of a circular cylinder (finite-le ngth section) are well modelled by a Ginzburg-Landau (GL) equation wit h zero boundary conditions (Albarede & Monkewitz 1992). According to t he GL model, the wake is mainly governed by a rescaled length, based o n the aspect ratio and the Reynolds number. However, the determination of coefficients is not complete: we correct a former evaluation of th e nonlinear Landau coefficient, we show difficulties in obtaining a co nsistent set of coefficients for different Reynolds numbers or end con figurations, and we propose the use of an 'influential' length. New tw o-point velocimetry results are presented: phase measurements show tha t 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. On ly the linear characteristics of the second mode are readily explained ; its existence depends on the end conditions. Moreover, through a qua si-static variation of the length, the second mode evolves continuousl y to end cells (and vice versa). Observations of the dislocated chevro n are recalled. A very similar instability is found on the chevron sol ution of the GL equation, when the model parameters (c(1), c(8)) move towards the phase diffusion unstable region. The early stages of this instability are qualitatively similar to the observed patterns.