Numerical study on instabilities behind a circular disk in a uniform flow

Instabilities behind a circular disk, which is normal to a uniform free-stream with aspect ratio of χ = 5, are numerically studied in the range of Re from 115 to 1000. The onsets of three characteristic instabilities including natural vortex shedding, shear-layer instability and a very low frequency instability, which are associated with the Reynolds number, are reported. When Re < 152, the wake stays steady and no vortex shedding occurs. A regular bifurcation leading to two-thread wake is observed for Re from 120 to 152. When Re increases to 152, the hairpin vortices begin to be periodically shed in a regular pattern. A reflectional-symmetry-breaking (RSB) mode is observed for Re from 152 to 155, a standing-wave (SW) mode is captured for Re from 156 to 247, and an unsteady state with planar symmetry and non-zero mean lift is captured for Re from 248 to 264. It is found that the hairpin vortices are always shedding in a fixed orientation for RSB mode, while shedding from diametrically opposite orientations at SW mode and the unsteady state with planar symmetry and non-zero mean lift. When Re increases to 265, a low frequency instability attributed to the irregular rotation of vortex shedding location is observed. The hairpin vortices are periodically shed in an irregular pattern and a new ‘4L’ vortex formation mode is identified. When Re increases to 650, the shear-layer instability starts to be detected in the shear layer. The critical Reynolds number is firstly identified in the range of 601–650. The cylindrical shear layer surrounding the vortex formation zone rolls up to form oblate ring vortices. The hairpin vortices break into pieces and small-scale vortices associated with the shear-layer instability are observed.