Dynamic Mode Decomposition of Flow Around a Circular Cylinder at a Subcritical Reynolds Number

Abstract

Flow around a circular cylinder is one of the canonical problems of fluid flows that has been widely studied due to its simple geometries. However, the underlying physics of flow past a circular cylinder is rather complicated. In the present study, flow around a circular cylinder at Re ≈ 3900 is investigated. The unsteady Reynolds-averaged Navier-Stokes (URANS) equations with the k-𝜔 SST turbulent model were employed. The proper orthogonal decomposition (POD), the dynamic mode decomposition (DMD), and the spectral orthogonal decomposition (SPOD) were performed to elucidate the underlying physics of fluid flows in a low-dimensional form. The mean flow structures were extracted through the first POD and DMD mode. The vortex shedding patterns can be detected by the second and third POD mode which are similar to the second mode pair of DMD. SPOD provides three vortex shedding structures from three dominant distinct frequencies. It also indicates that POD requires less modes to reconstruct the mean flow field compared to DMD. It is suggested that the first five most dominant POD modes are sufficient to perform flow reconstruction. The vortex shedding frequencies can be detected via DMD and SPOD.