POD Analysis of the Wake of Two Tandem Square Cylinders

This study aims to investigate the wake of two tandem square cylinders based on the Proper Orthogonal Decomposition (POD) analyses of the PIV and hotwire data. The cylinder centre-to-centre spacing ratio L/w examined is from 1.2 to 4.2, covering the four flow regimes, i.e., extended body, reattachment, transition and co-shedding. The Reynolds number examined was 1.3 × 10⁴. A novel Proper Orthogonal Decomposition (POD) technique (hereafter referred to as POD_HW) is developed to analyse data from single point hotwire measurements, offering a new perspective compared to the conventional POD analysis (POD_PIV) based on Particle Image Velocimetry (PIV) data. A key finding is the identification of two distinct states, reattachment and co-shedding, within the transition flow regime at L/w = 2.8, which POD_PIV fails to capture due to the limited duration of the PIV data obtained. This study confirms, for the first time, the existence of these states as proposed by Zhou et al. (2024), highlighting the advantage of using POD_HW for capturing intermittent flow phenomena. Furthermore, the analysis reveals how the predominant coherent structures contribute to the total fluctuating velocity energy in each individual regime. Other aspects of the flow are also discussed, including the Strouhal numbers, the contribution to the total fluctuating energy of the flow from the first four POD modes, and a comparison between different regimes.