Nozzle dynamics and wavepackets in turbulent jets

Abstract

We study a turbulent jet issuing from a cylindrical nozzle to characterise coherent structures evolving in the turbulent boundary layer. The analysis is performed using data from a large-eddy simulation of a \(M=0.4\) jet. Azimuthal decomposition of the velocity field in the nozzle shows that turbulent kinetic energy predominantly resides in high azimuthal wavenumbers; the first three azimuthal wavenumbers, that are important for sound generation, contain much lower, but non-zero amplitudes. Using two-point statistics, low azimuthal modes in the nozzle boundary layer are shown to exhibit significant correlations with modes of same order in the free-jet region. Spectral Proper Orthogonal Decomposition (SPOD) is used to distill a low-rank approximation of the flow dynamics. This reveals the existence of tilted coherent structures within the nozzle boundary layer and shows that these are coupled with wavepackets in the jet. The educed nozzle boundary-layer structures are modelled using a local linear stability analysis of the nozzle mean flow. Projection of the leading SPOD modes on the stability eigenmodes shows that the organised boundary-layer structures can be modelled using a small number of stable eigenmodes of the boundary-layer branch of the eigenspectrum, indicating the prevalence of non-modal effects. Finally local resolvent analysis of the mean-flow is performed. It is shown that the most-energetic nozzle structures can be succesfully described with optimal resolvent response modes, whose associated forcing modes are observed to tilt against the nozzle boundary-layer, suggesting that the Orr mechanism underpins these organised, turbulent, boundary-layer structures.