The identification of coherent structures using proper orthogonal decomposition and dynamic mode decomposition

Abstract

A comprehensive comparison was conducted on the identification of coherent structures in fluid flow using Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). The influences that multi-dominant structures and high-order harmonics had on the decomposed modes were taken into extensive consideration. To this end, a series of fabricated patterns was constructed for the benchmark testing to simulate multi-dominant convective structures superimposed in a stationary field. The comparison showed that the temporal DMD method could clearly separate each structure in the spatial and spectral senses, while the POD mode corresponding to the desired structure is contaminated by the other uncorrelated structures. Subsequently, two case studies of the real wake flows, which were determined from high-repetition TR-PIV measurements, were employed to demonstrate the discrepancies of the POD and DMD algorithms in extracting coherent structures. For the wake flow behind a single cylinder at ReD=8000, the temporal DMD algorithm accurately determined the frequency, wavelength and convection speed of the Karman-like vortex street and its higher-order harmonics. However, although the first two POD modes are closely related to the Karman-like vortex street, the higher POD modes embedded as larger structures are obscure in the physical significance. Finally, the wake flow behind two side-by-side cylinders of different diameters at ReD=1000 based on the diameter of the small cylinder was measured; two configurations with different gaps were chosen for comparison, i.e., G/D=0.5 and 2.0. For the wake flow at G/D=0.5, the POD and DMD algorithms determined the major features of the single-dominant structure. For the wake flow at G/D=2.0, the first and second temporal DMD modes effectively and independently extracted the Karman-like vortex structures behind the large and small cylinders, respectively. Meanwhile, although the first and second pairs of POD modes generally captured these two convecting structures, respectively, there was obvious existence of the undesirable contamination of the POD mode, as reflected in the interaction between the desired and uncorrelated structures.