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Experimental spatio-temporal flow data often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised or missing regions, a data completion method based on spectral proper orthogonal decomposition (SPOD) is developed. The algorithm leverages the temporal correlation of the SPOD modes with preceding and succeeding snapshots, and their spatial correlation with the surrounding data at the same time instant. For each gap, the algorithm first computes the SPOD of the remaining, unaffected data. In the next step, the compromised data are projected onto the basis of the SPOD modes. This corresponds to a local inversion of the SPOD problem and yields expansion coefficients that permit the reconstruction in the affected regions. This local reconstruction is successively applied to each gap. After all gaps are filled in, the procedure is repeated in an iterative manner until convergence. This method is demonstrated on two examples: direct numerical simulation of laminar flow around a cylinder, and time-resolved PIV data of turbulent cavity flow obtained by Zhang et al. (2019). Randomly added gaps correspond to 1%, 5%, and 20% of data loss. Even for 20% data corruption, and in the presence of measurement noise in the experimental data, the algorithm recovers 97% and 80% of the original data in the corrupted regions of the simulation and PIV data, respectively. These values are higher than those achieved by established methods like gappy POD and Kriging.

The mechanisms by which near-nozzle forcing alters the turbulence structure and far-field sound of turbulent jets are not well understood. We perform large-eddy simulations of subsonic and supersonic axisymmetric isothermal turbulent jets subjected to an axisymmetric periodic forcing. The triple decomposition framework and spectral proper orthogonal decomposition are used to study the effect of the forcing on the underlying turbulence spectrum and determine how the periodic forcing alters coherent non-phase-locked structures. For subsonic jets, high-amplitude (1% of the jet velocity) low-frequency, Stf = 0.3, forcing is required to achieve a small change to the underlying turbulence spectrum and most energetic modes of the subsonic jet, despite producing a very energetic, phase-locked (tonal) response. The changes in the spectrum and the phase-locked structures are predicted well via resolvent analysis and linearized Navier-Stokes computations performed on the new turbulent mean, respectively. This suggests that there is little nonlinear interaction between the phase-locked structures and natural turbulence. High-frequency forcing, Stf = 1.5, shows similarly linear behavior except for around St≈0.75, which appears to be associated with vortex pairings triggered by the natural turbulence. Results of a similar analysis performed on a Mach 1.5 ideally expanded isothermal jet will also be presented.