Spectral proper orthogonal decomposition analysis of coherent vortical structures in the wake of a rectangular cylinder

This study investigates the unsteady flow around a wall-mounted square cylinder (WMSC) with an aspect ratio of 7 at a Reynolds number of 12 000 using large eddy simulation with the wall-adapting local eddy-viscosity subgrid-scale model in OpenFOAM. To analyze dominant flow structures, spectral proper orthogonal decomposition (SPOD) is applied to 26 planes oriented in the x-, y-, and z-normal directions. The results reveal key shedding phenomena, including a primary vortex-shedding mode at a Strouhal number of ∼0.105 and a second-cell vortex shedding at St≈0.127. The second-cell vortex shedding is concentrated near the base and junction of the cylinder, with minimal influence from mid to tip regions. Additionally, a secondary tip vortex at St≈1.8 is identified in three dimensions, originating at the rooftop of leading edge and localized near the tip. To examine this high-frequency feature, both two-dimensional and three-dimensional SPOD analyses are performed. While two-dimensional SPOD captures localized high-frequency structures, full-domain three-dimensional SPOD shows these structures are often masked by more energetic low-frequency modes. However, restricting the three-dimensional SPOD domain to the tip region clearly distinguishes the secondary tip vortex from dominant wake shedding. These findings demonstrate multi-cell shedding patterns and distinct high-frequency vortical structures, challenging the assumption of a single dominant shedding mechanism behind WMSC. Identifying multiple coherent structures at different frequencies highlights the importance of spectral techniques in resolving turbulence interactions in finite cylinder wakes.