Global Mode Reconstruction using Phase-Consistent SPOD

Abstract

The reconstruction of globally consistent spectral proper orthogonal decomposition (SPOD) modes is demonstrated through the development of a phase-consistent SPOD (pcSPOD) scheme. The methodology developed is capable of producing estimates of global SPOD mode shapes from datasets that are gathered over multiple, time-independent, spatially-overlapping measurement windows. The resulting pcSPOD mode sets represent the dominant spatio-temporal dynamics across the entirety of domains considered. The pcSPOD methodology is extensible to any dataset that satisfies the basic requirements for SPOD viability and thus provides valuable insight into the key dynamics and features present in a number of statistically-stationary, oscillatory flowfields. To demonstrate the capability of pcSPOD for analyzing generic datasets, the technique is used to analyze a large eddy simulation (LES) of a turbulent jet and a direct numerical simulation (DNS) of laminar flow past a cylinder. The pcSPOD methodology is used to compare the reconstructed global SPOD mode shapes from multiple, time-independent measurement windows against the true, global SPOD modes from the original spatial domain. It is shown that the pcSPOD methodology successfully reconstructs the global structure of the the dominant SPOD modes for the cases investigated.