Numerical study on coherent structure behind a circular disk

A numerical study on the turbulent wake behind a circular disk of an aspect ratio 5 at Re=104 is performed. Three characteristic instabilities are confirmed, including a low-frequency instability at StL≈0.05-0.06 due to pumping motion of the recirculation region, large-scale vortex shedding at StV≈0.14, and the shear-layer instability at StKH≈1.4-1.6. A large waviness of the wake coherent structures is observed and further studied with the definition of the wake positions. It is suggested that the coexistence of lots of irregular helical/helical-like modes in the wake leads to the waviness. The traces of the wake positions in phase diagram could give a good description of the irregular motion of the large-scale vortex shedding location, which occurs at the same large-scale vortex shedding frequency. Two preferred states in the wake are found, which could induce two asymmetric topologies. The reflectional-symmetry-breaking regime at laminar wake is persistent in the turbulent wake and gives rise to the two asymmetric flow states. And, it is found that the coherent structure from the conditional averaging of each preferred state bears a remarkable resemblance to the wake structure at RSB mode for a low Reynolds number. Considering the topology from the conditional averaging of each preferred state and the flow visualizations at RSB mode, a spatial coherent wake structure at Re=104 is then proposed.