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

Abstract

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.