Modal Analysis of Fluid Flows: An Overview
arXiv:1702.01453
Abstract
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 flow field, 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. For a non-expert, 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.
arXiv comment43 pages, 17 figures
References in corpus (17)
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- Sparsity-promoting dynamic mode decomposition
- A critical layer model for turbulent pipe flow
- Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
- Chaos as an Intermittently Forced Linear System
- Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
- An Introduction to Adjoint Problems
- On coherent structure in wall turbulence
- Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
- Randomized Low-Rank Dynamic Mode Decomposition for Motion Detection
- Data Fusion via Intrinsic Dynamic Variables: An Application of Data-Driven Koopman Spectral Analysis
- Networked oscillator based modeling and control of unsteady wakes
- Multi-Resolution Dynamic Mode Decomposition
- Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence
- Projection-free approximate balanced truncation of large unstable systems
- Scaling and interaction of self-similar modes in models of high-Reynolds number wall turbulence
- Recursive dynamic mode decomposition of a transient cylinder wake