Frequency-time analysis, low-rank reconstruction and denoising of turbulent flows using SPOD

TL;DR

This paper demonstrates the use of spectral proper orthogonal decomposition (SPOD) for low-rank reconstruction, denoising, and frequency-time analysis of turbulent flows, proposing new methods for flow field reconstruction and noise reduction.

Contribution

It introduces novel SPOD-based approaches for flow reconstruction, denoising, and frequency-time analysis, including time-domain and frequency-domain strategies, applied to turbulent jet data.

Findings

SPOD-based low-rank reconstruction can be performed via direct spectral inversion.

A SPOD-based denoising strategy using eigenvalue thresholding significantly reduces noise.

Frequency-time analysis with SPOD reveals the link between large-scale structures and high-energy events.

Abstract

Four different applications of spectral proper orthogonal decomposition (SPOD): low-rank reconstruction, denoising, frequency-time analysis, and prewhitening are demonstrated on large-eddy simulation data of a turbulent jet. SPOD-based low-rank reconstruction can be performed by direct inversion of a truncated SPOD. This spectral inversion problem, however, is ambiguous since SPOD relies on spectral estimation. 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). While the SPOD optimally represents the flow in a statistical sense, the time-domain approach seeks an optimal reconstruction of each instantaneous flow field. We further propose 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. In contrast to standard methods of frequency-time analysis such as wavelet transform, a proposed SPOD-based approach yields a spectrogram that characterizes the temporal evolution of spatially coherent flow structures. In the frequency-domain, time-varying expansion coefficients can be obtained by basing the SPOD on a sliding window. This approach, however, is computationally intractable, and an alternative strategy based on convolution in the time-domain is presented. When applied to the turbulent jet data, SPOD-based frequency-time analysis reveals that the intermittent occurrence of large-scale coherent structures is directly associated with high-energy events. This work suggests that the time-domain approach is preferable for low-rank reconstruction of individual snapshots, and the frequency-domain approach for denoising and frequency-time analysis.