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It is well known that the flow around a sphere becomes steady and non-axisymmetric when the freestream Reynolds number (based on the diameter) becomes greater than 210. However such steady asymmetric patterns cannot be found in the case of the two-dimensional flow around a circular cylinder. In this paper, the flow around a three-dimensional low aspect ratio cylinder is calculated, and it is found that the flow around a low aspect ratio cylinder also becomes steady and asymmetric under a certain range of freestream Reynolds numbers. The two-dimensional and three-dimensional incompressible Navier-Stokes equations are numerically solved for flows around these bodies, and the transition mode from steady symmetric flow to asymmetric flow is investigated by global stability analysis. These results show that in the two-dimensional case, the asymmetric non-oscillatory mode decays faster than the oscillatory modes. In the case of the asymmetric non-oscillatory mode of the two-dimensional flow, the region of its influence extends far downstream and reaches the outer boundary of the computational domain, while in the three-dimensional non-oscillatory mode the region of influence is observed only in the vicinity of the body. The similarities of the flow around a sphere and low aspect ratio cylinder are discussed from a viewpoint of the configuration of these transition modes.

Global Stability Analysis of Asymmetric Flow around a Two-Dimensional Cylinder, a Sphere, and a Three-Dimensional Low Aspect Ratio Cylinder