Four different applications of spectral proper orthogonal decomposition (SPOD) are demonstrated on large-eddy simulation data of a turbulent jet. These are: low-rank reconstruction, denoising, frequency–time analysis and prewhitening. We demonstrate SPOD-based flow-field reconstruction using direct inversion of the SPOD algorithm (frequency-domain approach) and propose an alternative approach based on projection of the time series data onto the modes (time-domain approach). We further present a SPOD-based denoising strategy that is based on hard thresholding of the SPOD eigenvalues. The proposed strategy achieves significant noise reduction while facilitating drastic data compression.

Literature:

  • [PDF] [DOI] Nekkanti, A. and O. T. Schmidt. “Frequency–time analysis, low-rank reconstruction and denoising of turbulent flows using spod.” Journal of fluid mechanics 926 (2021): A26.
    [Bibtex] 
    @Article{nekkantischmidt_2021_jfm,
author = {Nekkanti, A. and Schmidt, O. T.},
journal = {Journal of Fluid Mechanics},
title = {Frequency–time analysis, low-rank reconstruction and denoising of turbulent flows using SPOD},
year = {2021},
pages = {A26},
volume = {926},
doi = {10.1017/jfm.2021.681},
file = {:NekkantiSchmidt_2021_JFM.pdf:PDF},
publisher = {Cambridge University Press},
}

Code:

Example 7 and routine tcoeffs.m in SPOD package on MATLAB Central File Exchange