Quasi-periodic cylinder wakes and the Ginzburg–Landau model

Abstract

The time-periodic phenomena occurring at low Reynolds numbers (Re [lsim ] 180) in the wake of a circular cylinder (finite-length section) are well modelled by a Ginzburg–Landau (GL) equation with zero boundary conditions (Albarède & Monkewitz 1992). 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 (c1, c2) move towards the phase diffusion unstable region. The early stages of this instability are qualitatively similar to the observed patterns.