Title: Spectral analysis of jet turbulence,
Abstract: 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.