Dynamic mode decomposition of numerical and experimental data

TLDR

Coherent features of fluid flow are essential for understanding fluid-dynamical and transport processes. The authors introduce a method that extracts dynamic information from flow fields generated by numerical simulation or measured in physical experiments. The method derives dynamic modes—generalizations of global stability modes—that describe underlying physical mechanisms, enable projection onto reduced dynamical systems, and allow localized instability analysis by focusing on subdomains, thereby illustrating its flexibility. The method is demonstrated on plane channel flow, flow over a two-dimensional cavity, wake behind a flexible membrane, and jet between two cylinders.

Abstract

The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders.