A comprehensive study of secondary and tertiary vortex phenomena of flow past a circular cylinder: A Cartesian grid approach

This study envisages undertaking a comprehensive simulation of the flow past an impulsively started circular cylinder with special emphasis on vortex dynamics in the secondary and tertiary level. A recently developed second order spatially and temporally accurate compact finite difference scheme on a nonuniform Cartesian grid has been used to discretize the transient Navier–Stokes equations governing the flow. The grid is generated in such a way that the cylinder boundary passes through the grid points, thus dispensing with the need to use the immersed interface approach on a Cartesian grid. High quality simulations are accomplished for a wide range of Reynolds numbers (Re) from 5 ≤ R e ≤ 10 000 in the laminar regime, including the periodic flow characterized by von Karman vortex street. The α, β, sub-α, and sub-β phenomena, which are the trademark of the secondary and tertiary vortex dynamics associated with such flows, are studied in detail. Our results are compared with existing experimental and numerical results, and close comparison is obtained in all the cases exemplifying their accuracy. In the process, for the first time, we also provide a tabular documentation of the early stages of the flow for R e ≥ 700.