Cyclostationary analysis of forced turbulent jets

We investigate the effect of harmonic acoustic forcing on turbulent jets using cyclostationary analysis, a statistical framework that accounts for the phase-dependent second-order statistics excluded by a statistically stationary description. Large-eddy simulations of a Mach 0.4 jet are performed with axisymmetric acoustic forcing at Strouhal 0.3 0.3 $0.3$ and 1.5 1.5 $1.5$ , and amplitudes up to 10 percent sign 10 % $10\,%$ of the jet velocity. Although forcing generates a strong tonal response and phase-dependent flow structures, its influence on the period-averaged mean flow and turbulence statistics is comparatively modest. Low-frequency forcing modifies the jet globally, whereas high-frequency forcing remains largely confined to the near-nozzle region. Only the strongest forcing produces substantial phase-dependent modulation of the local energy transfer between the mean and turbulent fields, yet the spatially integrated energy transfer varies only weakly over the forcing cycle. Coherent structures at low azimuthal mode order are analysed using cyclostationary spectral proper orthogonal decomposition, which enables the phase-dependent component of the turbulent statistics to be isolated and characterised. The dominant structures retain the wavepacket characteristics of the natural jet but acquire a phase dependence reflecting the periodic modulation of the mean flow. Overall, the results indicate that harmonic forcing modifies the coherent structures primarily through its influence on the underlying mean flow, while introducing only comparatively modest changes to the broadband turbulent dynamics, despite the strong tonal response and substantial local phase-dependent modulation observed at the highest forcing amplitude.