Benefits of FIR-based spectral proper orthogonal decomposition in separation of flow dynamics in the wake of a cantilevered square cylinder

A comparative analysis is presented to illustrate the benefits of finite impulse response (FIR)-based spectral proper orthogonal decomposition (SPOD) over traditional proper orthogonal decomposition (POD) in separating coherent contributions within narrow spectral bandwidth. The wake of a cantilevered square cylinder of height-to-width ratio h/d=4 protruding a thin laminar boundary layer (δ/d=0.21) is investigated at a Reynolds number (Re) of 10600 using time-resolved stereoscopic particle image velocimetry. In the vicinity of the obstacle-plate junction region (z<0.5d), spectral analysis of the temporal modes obtained with both POD and FIR-based SPOD show fluctuation energy concentration centered on the vortex shedding frequency (fs), as well as weaker contributions at 0.1, 0.4, 0.9, 0.95, 1.05, 1.1, and 2fs. Broad-band spectral energy concentrations around 0.4fs are mainly observed close to the ground plane, while the energy contents at (1±0.05)fs and (1±0.1)fs increase at higher planes. With POD, the frequencies are not separated in the modes and it is very difficult to associate each to specific phenomena within the wake region. However, with tuning of the filter bandwidth, FIR-based SPOD represents each of the identified frequencies in a separate mode pair, which permits a better interpretation of the related dynamics. Notably, the improved modal separation assists in associating the 0.4fs spectral contribution with the interactions between the extensions of horseshoe vortex system and Kármán vortices in the wall-body junction region and the (1±0.05)fs and (1±0.1)fs frequencies to perturbation of the shedding cycle resulting from interactions with the lower frequency dynamics.