Modal analysis of forced turbulent jets

A variety of actuation methods have been employed to force turbulent jets, where in addition to the strong deterministic tonal response, the underlying stochastic turbulence is modulated by the applied forcing. However, the impact of the forcing on the turbulence and coherent structures is lacking. Since the forcing modulates the turbulence, the flow can not be analyzed using tools such as spectral proper orthogonal decomposition (SPOD) and resolvent analysis that have been successful in studying the mechanisms and coherent structures present in the unforced flow since they rely on a statistically-stationary assumption. Instead, the turbulence is cyclostationary, meaning that the statistics vary periodically. We investigate the impact of the forcing using recent extensions to SPOD and resolvent analysis, called cyclostationary SPOD (CS-SPOD) and harmonic resolvent analysis, which are suitable for analyzing flows with periodically varying statistics. We perform large-eddy simulations of forced turbulent jets using low-frequency St_f=0.3 and high-frequency St_f=1.5 forcing at various amplitudes. We find that the coherent structures are modulated by the applied forcing at both forcing frequencies. Good agreement between the dominant coherent structures determined via CS-SPOD and those predicted by the linearized harmonic resolvent analysis are seen.