Tertiary wake mode in flows past elliptic cylinders

Abstract

Linear stability analysis of the steady flow past elliptic cylinders of different aspect ratio ($Ar$) has been conducted for the flow Reynolds number ($Re$) in the range 30–200. A new unstable mode, which we refer as tertiary wake mode, has been discovered. Two other unstable modes (the primary wake mode and the secondary wake mode), already reported in the literature, are also found. The critical $Re$ for the onset of instability of these modes and the corresponding Strouhal number ($St$) have been reported. Modes that have large growth rates tend to come close to the cylinder surface, and the extent to which they spread downstream in the wake is less compared to the weaker modes. The size of the vortical structures in a mode is inversely related to its $St$. The change in the characteristics of these modes with respect to change in $Ar$ and $Re$, as well as their evolution leading to the fully developed flow, has been studied. Selective suppression of the unstable modes is effected using a slip-plate placed on the wake centerline. For $Re$ = 150, it is shown that selective suppression of the unstable modes leads to different fully developed unsteady flows.