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Published December 2017 | public
Journal Article Open

Modal Analysis of Fluid Flows: An Overview


Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically important features, or modes, as a first step in the analysis. This step typically starts with a modal decomposition of an experimental or numerical dataset of the flowfield, or of an operator relevant to the system. We describe herein some of the dominant techniques for accomplishing these modal decompositions and analyses that have seen a surge of activity in recent decades [1–8]. For a nonexpert, keeping track of recent developments can be daunting, and the intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community. In particular, we present a brief overview of several of the well-established techniques and clearly lay the framework of these methods using familiar linear algebra. The modal analysis techniques covered in this paper include the proper orthogonal decomposition (POD), balanced proper orthogonal decomposition (balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global linear stability analysis, and resolvent analysis.

Additional Information

© 2017 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Publication Date (online): October 31, 2017. This paper was one of the major outcomes from the AIAA Discussion Group (Fluid Dynamics Technical Committee) entitled "Modal Decomposition of Aerodynamics Flows" organized by Kunihiko Taira and Douglas R. Smith [U.S. Air Force Office of Scientific Research (AFOSR) Program Officer, Unsteady Aerodynamics and Turbulent Flows]. D. R. Smith has been instrumental in creating, organizing, and supporting this discussion group at every stage. He, in fact, has been one of the contributors to the present overview paper from conception to final editing. We gratefully acknowledge the contributions made by D. R. Smith to this document and for his continued support of much of this work. The authors also thank the fruitful discussions with the members of the discussion group and greatly acknowledge the generous support from the following agencies: U.S. Air Force Office of Scientific Research, Army Research Office, Defense Advanced Research Projects Agency, U.S. Department of Energy, Deutsche Forschungsgemeinschaft, the European Office of Aerospace Research and Development, the National Science Foundation, and the Office of Naval Research. The authors acknowledge the anonymous referees for providing insightful comments on the paper. K. Taira is grateful to his research group members for providing extensive feedback throughout the preparation of this paper.

Attached Files

Erratum - 1.j056060.c1.pdf

Submitted - 1702.01453.pdf


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