A dynamic mode decomposition technique for the analysis of non-uniformly sampled flow data

A novel Dynamic Mode Decomposition (DMD) technique capable of handling non-uniformly sampled data is proposed. As it is usual in DMD analysis, a linear relationship between consecutive snapshots is made. The performance of the new method, which we term theta-DMD, is assessed on three different, increasingly complex datasets: a synthetic flow field, a Re-D = 60 flow around a cylinder cross section, and a Re-tau = 200 turbulent channel flow. For the three datasets considered, whenever the dataset is uniformly sampled, the theta-DMD method provides comparable results to the original DMD method. Additionally, the theta-DMD is still capable of recovering relevant flow features from non-uniformly sampled databases, whereas DMD cannot. The proposed tool opens the way to conduct DMD analyses for non-uniformly sampled data, and can be useful e.g., when confronted with experimental datasets with missing data, or when facing numerical datasets generated using adaptive time-integration schemes. (C) 2022 The Author(s). Published by Elsevier Inc.