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On the accuracy of dynamic mode decomposition in estimating instability of wave packet

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Abstract

Lots of unstable flows in both nature and engineering pose multi-scale perturbations with infinitesimal initial amplitude, which compete and interact with each other during their unstable evolution. Dynamic mode decomposition (DMD) analysis can be used to extract these components’ temporal/spatial growth rate. Therefore, it is necessary to evaluate the accuracy performance and confidence limit of DMD algorithm in the circumstance of multi-scale instability wave packet. In the present study, we use a linear combination of a sinusoidal unstable wave and its high-order harmonics as a prototype, based on which an error analysis of DMD algorithm is taken. In first, different numerical algorithms of DMD analysis are compared in terms of both accuracy and efficiency. The accuracy evaluation of the classical DMD algorithm in a large parameter domain is followed. It is found that the superimposition of finer structures with less energy dominance might damage the estimation accuracy of the primary structures’ growth rate. Strong evidences suggest that even in a linear circumstance, resolving the dynamics of small-scale structures is comparably more difficult than that of the primary structures, i.e., DMD algorithm has a preference for structures with energetic dominance. Finally, the recommended thresholds for the sampling/discretizing parameters are summarized for practical usage.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11372001 and 11327202).

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Authors and Affiliations

  1. Key Laboratory of Fluid Mechanics, Ministry of Education, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Chong Pan, Dong Xue & Jinjun Wang

Authors
  1. Chong Pan
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  2. Dong Xue
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  3. Jinjun Wang
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Correspondence to Chong Pan.

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Pan, C., Xue, D. & Wang, J. On the accuracy of dynamic mode decomposition in estimating instability of wave packet. Exp Fluids 56, 164 (2015). https://doi.org/10.1007/s00348-015-2015-6

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  • DOI: https://doi.org/10.1007/s00348-015-2015-6

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