Dynamic mode decomposition analysis of spatially agglomerated flow databases

Dynamic Mode Decomposition (DMD) techniques have risen as prominent feature identification methods in the field of fluid dynamics. Any of the multiple variables of the DMD method allows to identify meaningful features from either experimental or numerical flow data on a data-driven manner. Performing a DMD analysis requires handling matrices V ϵ R^np×N, where n_p and N are indicative of the spatial and temporal resolutions. The DMD analysis of a complex flow field requires long temporal sequences of well resolved data, and thus the memory footprint may become prohibitively large. In this contribution, the effect that principled spatial agglomeration (i.e., reduction in n_p via clustering) has on the results derived from the DMD analysis is investigated. We compare twelve different clustering algorithms on three testcases, encompassing different flow regimes: a synthetic flow field, a Re_D = 60 flow around a cylinder cross section, and a Re_τ ≈ 200 turbulent channel flow. The performance of the clustering techniques is thoroughly assessed concerning both the accuracy of the results retrieved and the computational performance. From this assessment, we identify DBSCAN/HDBSCAN as the methods to be used if only relatively high agglomeration levels are affordable. On the contrary, Mini-batch K-means arises as the method of choice whenever high agglomeration n_p/n_p&tild; < 1 is possible.