We discuss the spectral proper orthogonal decomposition and its use in identifying modes, or structures, in flow data. A specific algorithm based on estimating the cross-spectral density tensor with Welch’s method is presented, and we provide guidance on selecting data sampling parameters, and understanding tradeoffs amongst them in terms of bias, variability, aliasing, and leakage. Practical implementation issues, including dealing with large datasets, are discussed and illustrated with examples involving experimental and computational turbulent flow data.


  • [PDF] Schmidt, O. T. and T. Colonius. “Guide to spectral proper orthogonal decomposition.” Aiaa journal (2020): 1–11.
    title={Guide to Spectral Proper Orthogonal Decomposition},
    author={Schmidt, O. T. and Colonius, T.},
    journal={AIAA Journal},
    publisher={American Institute of Aeronautics and Astronautics}

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