SPOD is a Matlab implementation of the frequency domain form of proper orthogonal decomposition (POD, also known as principle component analysis or Karhunen-Loève decomposition) called spectral proper orthogonal decomposition (SPOD). SPOD is derived from a space-time POD problem for stationary flows and leads to modes that each oscillate at a single frequency. SPOD modes represent dynamic structures that optimally account for the statistical variability of stationary random processes.
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Schmidt, O. T., A. Towne, T. Colonius, A. V. G. Cavalieri, P. Jordan, and G. A. Brès. “Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability.” Journal of fluid mechanics 825 (2017): 1153-1181.
[Bibtex]@Article{SchmidtEtAl_2017_JFM, author = {Schmidt, O. T. and Towne, A. and Colonius, T. and Cavalieri, A. V. G. and Jordan, P. and Br{\`e}s, G. A.}, title = {Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability}, journal = {Journal of Fluid Mechanics}, year = {2017}, volume = {825}, pages = {1153-1181}, doi = {10.1017/jfm.2017.407}, file = {:SchmidtEtAl_2017_JFM.pdf:PDF}, publisher = {Cambridge University Press}, } - Taira, K., S. L. Brunton, S. Dawson, C. W. Rowley, T. Colonius, B. J. McKeon, O. T. Schmidt, S. Gordeyev, V. Theofilis, and L. S. Ukeiley. “Modal analysis of fluid flows: an overview.” Aiaa journal (2017).
[Bibtex]@Article{TairaEtAl_2017_AIAAJ, author = {Taira, K. and Brunton, S. L. and Dawson, S. and Rowley, C. W. and Colonius, T. and McKeon, B. J. and Schmidt, O. T. and Gordeyev, S. and Theofilis, V. and Ukeiley, L. S.}, title = {Modal analysis of fluid flows: An overview}, journal = {AIAA Journal}, year = {2017}, doi = {https://doi.org/10.2514/1.J056060}, file = {:TairaEtAl_2017_AIAAJ.pdf:PDF}, } - Towne, A., O. T. Schmidt, and T. Colonius. “Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis.” Journal of fluid mechanics 847 (2018): 821–867.
[Bibtex]@Article{TowneSchmidtColonius_2018_JFM, author = {Towne, A. and Schmidt, O. T. and Colonius, T.}, title = {Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis}, journal = {Journal of Fluid Mechanics}, year = {2018}, volume = {847}, pages = {821–867}, doi = {10.1017/jfm.2018.283}, file = {:TowneSchmidtColonius_2018_JFM.pdf:PDF}, publisher = {Cambridge University Press}, } - Schmidt, O. T., A. Towne, G. Rigas, T. Colonius, and G. A. Brès. “Spectral analysis of jet turbulence.” Journal of fluid mechanics 855 (2018): 953–982.
[Bibtex]@Article{SchmidtEtAl_2018_JFM, author = {Schmidt, O. T. and Towne, A. and Rigas, G. and Colonius, T. and Br{\`e}s, G. A.}, title = {Spectral analysis of jet turbulence}, journal = {Journal of Fluid Mechanics}, year = {2018}, volume = {855}, pages = {953–982}, doi = {10.1017/jfm.2018.675}, file = {:SchmidtEtAl_2018_JFM.pdf:PDF}, publisher = {Cambridge University Press}, } - Schmidt, O. T. and A. Towne. “An efficient streaming algorithm for spectral proper orthogonal decomposition.” Computer physics communications (2018).
[Bibtex]@Article{SchmidtTowne_2018_CPC, author = {Schmidt, O. T. and Towne, A.}, title = {An efficient streaming algorithm for spectral proper orthogonal decomposition}, journal = {Computer Physics Communications}, year = {2018}, issn = {0010-4655}, abstract = {A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated cross-spectral density (CSD) matrix is performed. The algorithm requires access to only one temporal snapshot of the data at a time and converges orthogonal sets of SPOD modes at discrete frequencies that are optimally ranked in terms of energy. We define measures of error and convergence, and demonstrate the algorithm’s performance on two datasets. The first example considers a high-fidelity numerical simulation of a turbulent jet, and the second example uses optical flow data obtained from high-speed camera recordings of a stepped spillway experiment. For both cases, the most energetic SPOD modes are reliably converged. The algorithm’s low memory requirement enables real-time deployment and allows for the convergence of second-order statistics from arbitrarily long streams of data. A MATLAB implementation of the algorithm along with a test database for the jet example, can be found in the Supplementary material.}, doi = {https://doi.org/10.1016/j.cpc.2018.11.009}, file = {:SchmidtTowne_2018_CPC.pdf:PDF}, keywords = {Proper orthogonal decomposition, Principal component analysis, Spectral analysis}, url = {http://www.sciencedirect.com/science/article/pii/S0010465518304016},}