A study for enhancing accuracy of POD analysis for near wake behind circular cylinder

This study performs a parametrical study of the proper orthogonal decomposition (POD) for the near wake behind a circular cylinder. Two cases with Reynolds numbers (Re, based on the cylinder diameter) of 3840 and 9440 are tested. The study confirms that the field of view (FOV) must not be less than the maximum spacing ($\lambda$) between the vortices in the K$\acute{a}$rm$\acute{a}$n vortex street and the FOV should be as close to $\lambda$ as possible to provide better image solution in the measurement using the particle image velocimetry (PIV) for the POD analysis. The accuracy of the PIV measurement determines the minimum number of image pairs (MT) that is required to achieve statistically stationary results for the POD analysis. It shows that 14000 < MT < 260000 at different upstream subregions for the two tested cases. A criterion based on the accuracy of the PIV measurement is proposed to determine the number of leading modes (m) for the low dimensional representation of fluid dynamics. The study shows that the values of MT and m increase as Re increases and m $\ll MT$. Moreover, the MT value increases as the subregion of interest moves to more downstream of wake flow due to decay of the K$\acute{a}$rm$\acute{a}$n vortex street.