Informed by LES data and resolvent analysis of the mean flow, we examine the structure of turbulence in jets in the subsonic, transonic, and supersonic regimes. Spectral (frequency-space) proper orthogonal decomposition is used to extract energy spectra and decompose the flow into energy-ranked coherent structures. The educed structures are generally well predicted by the resolvent analysis. Over a range of low frequencies and the first few azimuthal mode numbers, these jets exhibit a low-rank response characterized by Kelvin-Helmholtz (KH) type wavepackets associated with the annular shear layer up to the end of the potential core and that are excited by forcing in the very-near-nozzle shear layer. These modes too the have been experimentally observed before and predicted by quasi-parallel stability theory and other approximations–they comprise a considerable portion of the total turbulent energy. At still lower frequencies, particularly for the axisymmetric mode, and again at high frequencies for all azimuthal wavenumbers, the response is not low rank, but consists of a family of similarly amplified modes. These modes, which are primarily active downstream of the potential core, are associated with the Orr mechanism. They occur also as sub-dominant modes in the range of frequencies dominated by the KH response. Our global analysis helps tie together previous observations based on local spatial stability theory, and explains why quasi-parallel predictions were successful at some frequencies and azimuthal wavenumbers, but failed at others.

The video shows, in quick succession, the raw LES data, a single Fourier component for m=0, and the leading SPOD mode at the same frequency. The streamwise perturbation velocity is visualized.

**Literature:**

- Schmidt, O. T., A. Towne, G. Rigas, T. Colonius, and G. A. Brès. “Spectral analysis of jet turbulence.” Journal of fluid mechanics 855 (2018): 953–982.

[Bibtex]`@Article{SchmidtEtAl_2018_JFM, author = {Schmidt, O. T. and Towne, A. and Rigas, G. and Colonius, T. and Br{\`e}s, G. A.}, title = {Spectral analysis of jet turbulence}, journal = {Journal of Fluid Mechanics}, year = {2018}, volume = {855}, pages = {953–982}, doi = {10.1017/jfm.2018.675}, file = {:SchmidtEtAl_2018_JFM.pdf:PDF}, publisher = {Cambridge University Press}, }`