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Dynamic Mode Decomposition (DMD) is a data-driven and model-freedecomposition technique. It is suitable for revealing spatio-temporal featuresof both numerically and experimentally acquired data. Conceptually, DMDperforms a low-dimensional spectral decomposition of the data into thefollowing components: The modes, called DMD modes, encode the spatialcontribution of the decomposition, whereas the DMD amplitudes specify theirimpact. Each associated eigenvalue, referred to as DMD eigenvalue,characterizes the frequency and growth rate of the DMD mode. In this paper, wedemonstrate how the components of DMD can be utilized to obtain temporal andspatial information from time-dependent flow fields. We begin with thetheoretical background of DMD and its application to unsteady flow. Next, weexamine the conventional process with DMD mathematically and put it inrelationship to the discrete Fourier transform. Our analysis shows that thecurrent use of DMD components has several drawbacks. To resolve these problemswe adjust the components and provide new and meaningful insights into thedecomposition: We show that our improved components describe the flow moreadequately. Moreover, we remove redundancies in the decomposition and clarifythe interplay between components, allowing users to understand the impact ofcomponents. These new representations ,which respect the spatio-temporalcharacter of DMD, enable two clustering methods that segment the flow intophysically relevant sections and can therefore be used for the selection of DMDcomponents. With a number of typical examples, we demonstrate that thecombination of these techniques allow new insights with DMD for unsteady flow.

Visualization and Selection of Dynamic Mode Decomposition Components for Unsteady Flow