A Dual-Time Implementation of the Spectral Proper Orthogonal Decomposition

The present work introduces a novel implementation of the Spectral Proper Orthogonal Decomposition (SPOD) which does not require fully-time-resolved flow field data. This implementation leverages a different sampling strategy, defined \emph{dual-time} sampling, than the conventional SPOD implementation, based on the \emph{time-resolved} data, to construct the cross-spectral density matrix in statistically stationary flows. Instead of requiring fully-resolved time series, the dual-time sampling strategy is based on sampling matching pairs of flow field snapshots separated by a variable time interval equal to the desired sampling intervals of the frequencies to be resolved. For statistically stationary flows, this allows the estimation of the spatiotemporal correlation matrix, and thus of the cross-spectral density matrix, without accessing time series. Despite being more data and computationally intensive than the conventional implementation, the proposed implementation allows the computation of the SPOD from measurement systems that cannot access time-resolved time series of the field. An example is low-repetition-rate Particle Image Velocimetry (PIV), which can only provide flow field snapshots. Dual-time sampling, using a double PIV system, paired with the present SPOD implementation would provide access to spectral analysis even in high-speed flows with a higher spatial resolution than the one provided by common high-repetition-rate systems.