Application of spectral proper orthogonal decomposition and resolvent analysis to periodically forced turbulent jets

While passive and active control strategies have been applied to turbulent jets to reduce their radiated sound, the mechanisms by which the forcing alters the turbulence and far-field sound are poorly understood. We perform large-eddy simulations of axisymmetric turbulent jets subjected to axisymmetric periodic forcing at multiple frequencies and amplitudes. Spectral proper orthogonal decomposition is used to study the effect of the forcing on the turbulence spectrum. Low-frequency forcing, St_f=0.3, while producing highly energetic tonal structures, has a limited effect upon the underlying turbulence spectrum of the jet and the most energetic modes. High levels of forcing, 1% of the jet velocity, are required to achieve a small change to the turbulent mean flow and a minor shift in the turbulence spectrum. The changes in the spectrum and the shift in the modes are predicted well via the resolvent analysis performed on the new turbulent mean flow. This suggests that there is little nonlinear interaction between the phase-locked structures and the natural turbulence. High-frequency forcing, St_f=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.