Extracting dominant dynamics about unsteady base flows

A wide range of techniques exist for extracting the dominant flow dynamics and features about steady, or periodic base flows. However, there have been limited efforts in extracting the dominant dynamics about unsteady, aperiodic base flow. These flows appear in many applications such as when there is a sudden change in the flow rate through a pipe, when an airfoil experiences stall, or when a vortex forms. For these unsteady flows, it is valuable to know not only the dynamics of the base flow but also the features that form around this base flow. Here, we discuss the current state of research on extracting important flow structures and their dynamics in such cases with time-varying base flows. In particular, we consider data-driven decompositions, operator-based methods, causality analysis, and some other approaches. We also offer an outlook and call attention to key areas that require future efforts.