Spacetime-spectral analysis of flowfields

Abstract

The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time dependence of the spectrum remains inaccessible. There exist various time-frequency analysis techniques, such as the short time fast Fourier transform and wavelets, but those are fundamentally limited in achieving high resolution in both the time and frequency domains concurrently. For spatiotemporal flowfields, the frequency based modal decompositions generally provide spatial modes with a temporal counterpart that evolves at a constant frequency. However, an accurate time-local spectral contribution and its variation over time are highly desired to better understand the intermittent/extreme events, for instance, in turbulent flowfields. To this end, this paper presents a spectral mode decomposition that yields spectral-space and spectral-time modes, where the latter along with the associated spectral energies provide a spectrogram that is at the resolution of flowfields. The spectral modes get both the frequency and energy ranks. The numerical examples demonstrate the use of technique not only in spacetime-frequency analysis but also in reduced-order modeling and denoising applications.