Frequency-time analysis of turbulent flows using spectral POD

Intermittency is an inherent feature of turbulent flows that describes the occurrence of flow events at irregular intervals. A common approach for the characterization of intermittent behaviour is frequency-time analysis. The standard tools of frequency-time analysis are wavelet and short-time Fourier transforms, which are applied to 1-D time series and quantify intermittency locally. In this work, we propose a method that identifies the intermittency of spatially coherent flow structures identified by spectral proper orthogonal decomposition (SPOD). The SPOD-based frequency-time analysis provides spectrograms that characterize the temporal evolution of the SPOD modes. This requires the computation of time-continuous expansion coefficients, which can in principle be obtained from a SPOD with a sliding window. This approach, however, is computationally intractable even for moderately-sized data. To mitigate this limitation, we propose an alternative strategy based on convolution in the time domain. We demonstrate this approach on large-eddy simulation data of a turbulent jet. The SPOD-based frequency-time analysis reveals that the intermittent occurrence of large-scale coherent structures is directly associated with high-energy events.