The dynamic feedback cycle of the two-dimensional Kármán vortex street

Abstract

This paper analyzes the complete process of the generation, development, and maintenance of the two-dimensional Kármán vortex street numerically. The vorticity-stream function equation is solved to simulate the flow field and analyze the temporal and spatial evolution of disturbances globally. By doing these, we have explored whether the disturbances are only generated from the upstream region initially or also include feedback processes from the downstream flow field. We find a new dynamic process of a feedback cycle, which could sustain the asymmetrical Kármán vortex street. Specifically, the small asymmetrical disturbances generate the asymmetrical vortex street initially and propagate to downstream regions. Importantly, these down-propagating disturbances also feed back to the upstream region with a larger amplitude and dominate later disturbances to sustain the pattern of the vortex street. Furthermore, we further verify that the upstream flow information does have an impact on the downstream flow field with two mixed flow fields simulated. In conclusion, the upstream and downstream disturbances coexist and influence each other, forming a stable dynamic cycle to sustain the pattern of the vortex street.