Global wake instabilities of low aspect-ratio flate-plates

Abstract

This paper investigates the linear destabilization of three-dimensional steady wakes developing behind flate plates placed normal to the incoming flow. Plates characterized by low length-to-width ratio $L$ are considered here. By varying this aspect ratio in the range $1 \le L \le 6$ three destabilization scenarios are identified. For very low aspect ratio $1 \le L \le 2$, the flow is first destabilized, when increasing the Reynolds number,by a steady global mode that breaks the top/bottom planar reflectional symmetry. The symmetric steady flow bifurcates, via a pitchfork bifurcation, towards an asymmetric steady wakes, similarly to the case of axisymmetric wakes behind sphere and disks. For long aspect ratio, $2.5 \le L \le 6$, the first unstable mode also breaks the top/bottom symmetry but is unsteady. A Hopf bifurcation occurs, as for the wake developing behind a two-dimensional circular cylinder. Finally an intermediate regime $2 \le L \le 2.5$ is found for which the flow gets first unstable to an unsteady mode that breaks the left/right planar reflectional symmetry.