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Experiments in Fluids

, Volume 50, Issue 4, pp 1123–1130 | Cite as

Application of the dynamic mode decomposition to experimental data

  • Peter J. SchmidEmail author
Research Article

Abstract

The dynamic mode decomposition (DMD) is a data-decomposition technique that allows the extraction of dynamically relevant flow features from time-resolved experimental (or numerical) data. It is based on a sequence of snapshots from measurements that are subsequently processed by an iterative Krylov technique. The eigenvalues and eigenvectors of a low-dimensional representation of an approximate inter-snapshot map then produce flow information that describes the dynamic processes contained in the data sequence. This decomposition technique applies equally to particle-image velocimetry data and image-based flow visualizations and is demonstrated on data from a numerical simulation of a flame based on a variable-density jet and on experimental data from a laminar axisymmetric water jet. In both cases, the dominant frequencies are detected and the associated spatial structures are identified.

Keywords

Shear Layer Proper Orthogonal Decomposition Proper Orthogonal Decomposition Mode Dynamic Mode Decomposition Arnoldi Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

Support from the Agence Nationale de la Recherche (ANR) through their “chaires d’excellence” program and from the Alexander-von-Humboldt Foundation is gratefully acknowledged.

References

  1. Bagheri S, Schlatter P, Schmid PJ, Henningson DS (2009) Global stability of a jet in crossflow. J Fluid Mech 624:33–44CrossRefzbMATHMathSciNetGoogle Scholar
  2. Berkooz G, Holmes P, Lumley JL (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Ann Rev Fluid Mech 25:539–575CrossRefzbMATHMathSciNetGoogle Scholar
  3. Edwards WS, Tuckerman LS, Friesner RA Sorensen DC (1994) Krylov methods for the incompressible Navier-Stokes equations. J Comp Phys 110:82–102CrossRefzbMATHMathSciNetGoogle Scholar
  4. Gallaire F, Chomaz J-M (2003) Mode selection in swirling jet experiments: a linear stability analysis. J Fluid Mech 494:223–253CrossRefzbMATHMathSciNetGoogle Scholar
  5. Greenbaum A (1997) Iterative methods for solving linear systems. SIAM Publishing, PhiladelphiazbMATHGoogle Scholar
  6. Lehoucq RB, Scott JA (1997) Implicitly restarted Arnoldi methods and subspace iteration. SIAM J Matrix Anal Appl 23:551–562CrossRefGoogle Scholar
  7. Lumley JL (1970) Stochastic tools in turbulence. Academic Press, USAzbMATHGoogle Scholar
  8. Noack BR, Afanasiev K, Morzynski M, Tadmor G, Thiele F (2003) A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J Fluid Mech 497:335–363CrossRefzbMATHMathSciNetGoogle Scholar
  9. Rowley C, Mezic I, Bagheri S, Schlatter P, Henningson DS (2009) Spectral analysis of nonlinear flows. J Fluid Mech 641:115–127CrossRefzbMATHMathSciNetGoogle Scholar
  10. Ruhe A (1984) Rational Krylov sequence methods for eigenvalue computation. Lin Alg Appl 58:279–316CrossRefMathSciNetGoogle Scholar
  11. Schmid PJ, Henningson DS (2001) Stability and transition in shear flows. Springer Verlag, New YorkzbMATHGoogle Scholar
  12. Schmid PJ, Sesterhenn JL (2008) Dynamic mode decomposition of numerical and experimental data. Bull Am Phys Soc, San Antonio/TXGoogle Scholar
  13. Schmid PJ (2010) Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 656:5–28Google Scholar
  14. Sirovich L (1987) Turbulence and the dynamics of coherent structures. Quart. Appl Math 593:333–358Google Scholar
  15. Theofilis V (2000) Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog Aerosp Sci 39:249–315CrossRefGoogle Scholar
  16. Trefethen LN, Bau D (1997) Numerical linear algebra. SIAM Publishing, PhiladelphiaCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Laboratoire d’Hydrodynamique (LadHyX)Ecole PolytechniquePalaiseauFrance

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