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Spectral analysis of jet turbulence

Published online by Cambridge University Press:  21 September 2018

Oliver T. Schmidt Open the ORCID record for Oliver T. Schmidt [Opens in a new window] ,
Aaron Towne Open the ORCID record for Aaron Towne [Opens in a new window] ,
Georgios Rigas Open the ORCID record for Georgios Rigas [Opens in a new window] ,
Tim Colonius  and
Guillaume A. Brès Open the ORCID record for Guillaume A. Brès [Opens in a new window]
Oliver T. Schmidt*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Aaron Towne
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
Georgios Rigas
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Guillaume A. Brès
Affiliation:
Cascade Technologies Inc., Palo Alto, CA 94303, USA
*
†Email address for correspondence: [email protected]
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Abstract

Informed by large-eddy simulation (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 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 subdominant 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.

JFM classification

Instability: Absolute/convective instability Acoustics: Jet noise Turbulent Flows: Shear layer turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 953 - 982
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Copyright
© 2018 Cambridge University Press 

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Footnotes

‡

Present address: Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093, USA.

§

Present address: Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.

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