An acoustically-tuned spectral proper orthogonal decomposition

A new method to construct efficient reduced-order models for far-field radiation from a turbulent round jet over a wide band of frequencies and directivity angles is proposed here. It leverages the property of the free-space Green’s function, often employed in the solution to the Lighthill's equation, in extracting the acoustic component from the Lighthill's equivalent near-field sources. The methodology is referred to here as the “Lighthill Spectral Proper Orthogonal Decomposition” or LSPOD. The process yields sharply low-rank LSPOD modes that recovers up to 95% of the acoustic fluctuations energy with just five modes for St ≲ 1. The LSPOD mode shapes resemble acoustic waves emanating from the jet’s breakdown location, very different to the wavepacket shapes of typical near-field fluctuations-based SPOD modes. Remarkably, the leading LSPOD mode alone reconstructs the far-field spectra at the peak radiation angle of ϕ = 30° to within 1 dB accuracy across all frequencies considered here. In fact, the OASPL results show that eight LSPOD modes are able to consistently recover the radiated sound pressure at all observer angles, even at sideline and upstream angles, within a single decibel error.