Global wake instabilities of low aspect-ratio flat-plates

Abstract

This paper investigates the linear destabilization of three-dimensional steady wake flows developing behind rectangular plates, which are oriented perpendicularly to the uniform incoming flow. The thickness-to-width ratio of plates is fixed to 1/6, while the length-to-width ratio L is varied in the range 1≤L≤6. For sufficiently low Reynolds numbers, three-dimensional steady wake flows are stable and exhibit two reflectional planar symmetries. Using extensive parallel numerical computations, global stability analysis of the fully three-dimensional steady base flows is systematically performed to determine the neutral curves of least stable global modes in the control parameters space. Three destabilization scenarios are thus identified. For very low aspect ratios 1≤L≤2, the flow is first destabilized, when increasing the Reynolds number, by a steady global mode which breaks the top/bottom planar reflectional symmetry of the steady base flow. The first three-dimensional wake flow bifurcation is thus a (planar) pitchfork bifurcation, similar to the (circle) pitchfork bifurcation of axisymmetric wakes developing behind sphere and disks. For long aspect ratios 2.5≤L≤6, the flow is first destabilized by an unsteady global mode, which also breaks the top/bottom symmetry. The first three-dimensional wake flow bifurcation is then a Hopf bifurcation, as in the case of two-dimensional wake flows developing behind infinitely elongated cylinders. For intermediate values of the aspect ratio 2≤L≤2.5, a novel wake destabilization scenario is found: a Hopf bifurcation which breaks the left/right planar reflectional symmetry. Finally, the number of global modes getting unstable in a narrow range of Reynolds number gives an insight of the rich and complex nonlinear dynamics of those wake flows.