Stable state of Mode A for flow past a circular cylinder

Abstract

A stable three-dimensional (3D) wake structure for flow past a circular cylinder has been discovered through 3D direct numerical simulations (DNS). The stable 3D wake structure occurs over a small range of Reynolds number (Re) below the critical Re for Mode A∗ (i.e., Mode A with large-scale vortex dislocations, where Mode A is the first 3D instability mode which will evolve into Mode A∗) instability. It is believed that the stable 3D wake structure discovered in this study is the stable state of Mode A wake structure inferred by Williamson [“Three-dimensional wake transition,” J. Fluid Mech. 328, 345–407 (1996)]. This confirms the wake transition sequence of 2D → A → A∗ → B suggested by Williamson. Compared with conventional Mode A structure, the stable state of Mode A structure has much weaker amplitude and does not evolve into large-scale vortex dislocations. The stable state of Mode A structure is triggered by small-scale spanwise disturbance introduced upstream of the cylinder, due to energy amplification through convective instability of the flow. The stable state of Mode A is transient and is damped out eventually under a transient initial disturbance condition, but is sustained throughout under a persistent disturbance condition. The emergence of the stable state of Mode A structure is correlated with both Re and the disturbance level. With the decrease of Re, the stable state of Mode A structure gradually becomes less well-defined and eventually disappears. With the decrease of the disturbance level, the stable state of Mode A structure emerges at a higher Re.