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Spectral Analysis of Jet Turbulence

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:

  • [PDF] [DOI] 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},
    }

Wavepackets and trapped acoustic modes in turbulent jets

Coherent features of a turbulent Mach 0.9, Reynolds number 1M jet are educed from a high-fidelity large eddy simulation. Besides the well-known Kelvin-Helmholtz instabilities of the shear-layer, a new class of trapped acoustic waves is identified in the potential core. In two parallel studies, we investigate these trapped acoustic waves using different techniques.

The video shows a trapped acoustic mode in the potential core of a Mach 0.9 turbulent jet obtained from a global stability analysis of the mean flow.

Literature:

  • [PDF] [DOI] Schmidt, O. T., A. Towne, T. Colonius, A. V. G. Cavalieri, P. Jordan, and G. A. Brès. “Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability.” Journal of fluid mechanics 825 (2017): 1153-1181.
    [Bibtex]
    @Article{SchmidtEtAl_2017_JFM,
    author = {Schmidt, O. T. and Towne, A. and Colonius, T. and Cavalieri, A. V. G. and Jordan, P. and Br{\`e}s, G. A.},
    title = {Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability},
    journal = {Journal of Fluid Mechanics},
    year = {2017},
    volume = {825},
    pages = {1153-1181},
    doi = {10.1017/jfm.2017.407},
    file = {:SchmidtEtAl_2017_JFM.pdf:PDF},
    publisher = {Cambridge University Press},
    }
  • [PDF] [DOI] Towne, A., A. V. G. Cavalieri, P. Jordan, T. Colonius, O. T. Schmidt, V. Jaunet, and G. A. Brès. “Acoustic resonance in the potential core of subsonic jets.” Journal of fluid mechanics 825 (2017): 1113-1152.
    [Bibtex]
    @Article{TowneEtAl_2017_JFM,
    author = {Towne, A. and Cavalieri, A. V. G. and Jordan, P. and Colonius, T. and Schmidt, O. T. and Jaunet, V. and Br{\`e}s, G. A.},
    title = {Acoustic resonance in the potential core of subsonic jets},
    journal = {Journal of Fluid Mechanics},
    year = {2017},
    volume = {825},
    pages = {1113-1152},
    doi = {10.1017/jfm.2017.346},
    file = {:TowneEtAl_2017_JFM.pdf:PDF},
    publisher = {Cambridge University Press},
    }

Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis

We consider the frequency domain form of proper orthogonal decomposition (POD) called spectral proper orthogonal decomposition (SPOD). SPOD is derived from a space-time POD problem for stationary flows and leads to modes that each oscillate at a single frequency. We establish a relationship between SPOD and dynamic mode decomposition (DMD); we show that SPOD modes are in fact optimally averaged DMD modes obtained from an ensemble DMD problem for stationary flows. Finally, we establish a connection between SPOD and resolvent analysis. The key observation is that the resolvent-mode expansion coefficients, which are usually treated as deterministic quantities described by an amplitude and phase, should be regarded as statistical quantities, described by their cross-spectral density, in order for the resolvent-mode expansion to properly capture the flow statistics. When the expansion coefficients are uncorrelated, we show that SPOD and resolvent modes are identical.

Literature:

  • [PDF] [DOI] Towne, A., O. T. Schmidt, and T. Colonius. “Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis.” Journal of fluid mechanics 847 (2018): 821–867.
    [Bibtex]
    @Article{TowneSchmidtColonius_2018_JFM,
    author = {Towne, A. and Schmidt, O. T. and Colonius, T.},
    title = {Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis},
    journal = {Journal of Fluid Mechanics},
    year = {2018},
    volume = {847},
    pages = {821–867},
    doi = {10.1017/jfm.2018.283},
    file = {:TowneSchmidtColonius_2018_JFM.pdf:PDF},
    publisher = {Cambridge University Press},
    }

Stability, Receptivity and Transition of Compressible Corner Flows

The corner flow problem is a generic model for wing-fuselage intersections, rotor-hub junctions, and supersonic engine inlets. Corner flows have been subject to more than six decades of extensive study, in particular because of their importance to the aeronautical industry.

Our research focuses on the stability and transition of compressible corner flows using direct numerical simulation and linear theory. The key contributions to the understanding of corner flows are a detailed study of the effect of compressibility on their stability that lead to the discovery of a new modal instability mechanism at supersonic speeds, and an in-depth investigation of a non-modal mechanism that explains the flow’s sensitivity and early transition. The relevance of this mechanism became apparent in the first direct numerical simulations of laminar-turbulent transition in corner flows.

The video shows a direct numerical simulation of the symmetric transition scenario in terms of isosurfaces of the Lambda2 vortex criterion.

Literature:

  • [PDF] [DOI] Schmidt, O. T. and U. Rist. “Linear stability of compressible flow in a streamwise corner.” Journal of fluid mechanics 688 (2011): 569-590.
    [Bibtex]
    @Article{SchmidtRist_2011_JFM,
    Title = {Linear stability of compressible flow in a streamwise corner},
    Author = {Schmidt, O. T. and Rist, U.},
    Journal = {Journal of Fluid Mechanics},
    Year = {2011},
    Pages = {569-590},
    Volume = {688},
    Doi = {10.1017/jfm.2011.405},
    File = {:./SchmidtRist_2011_JFM.pdf:PDF},
    Publisher = {Cambridge Univ Press}
    }
  • [PDF] [DOI] Schmidt, O. T., B. Selent, and U. Rist. “Direct numerical simulation of boundary layer transition in streamwise corner-flow.” High performance computing in science and engineering (2013): 337-348.
    [Bibtex]
    @Article{SchmidtRistSelent_2013_HPCSE,
    author = {Schmidt, O. T. and Selent, B. and Rist, U.},
    title = {Direct numerical simulation of boundary layer transition in streamwise corner-flow},
    journal = {High Performance Computing in Science and Engineering},
    year = {2013},
    pages = {337-348},
    doi = {10.1017/S0022112095003284},
    file = {:SchmidtRistSelent_2013_HPCSE.pdf:PDF},
    owner = {iagoschm},
    publisher = {Cambridge Univ Press},
    }
  • [PDF] [DOI] Schmidt, O. T. and U. Rist. “Viscid–inviscid pseudo-resonance in streamwise corner flow.” Journal of fluid mechanics 743 (2014): 327–357.
    [Bibtex]
    @Article{SchmidtRist_2014_JFM,
    author = {Schmidt, O. T. and Rist, U.},
    title = {Viscid--inviscid pseudo-resonance in streamwise corner flow},
    journal = {Journal of Fluid Mechanics},
    year = {2014},
    volume = {743},
    pages = {327--357},
    doi = {10.1017/jfm.2014.31},
    file = {:SchmidtRist_2014_JFM.pdf:PDF},
    publisher = {Cambridge Univ Press},
    }
  • [PDF] [DOI] Schmidt, O. T., S. M. Hosseini, Ulrich Rist, A. Hanifi, and D. S. Henningson. “Optimal wavepackets in streamwise corner flow.” Journal of fluid mechanics 766 (2015): 405–435.
    [Bibtex]
    @Article{SchmidtEtAl_2015_JFM,
    Title = {Optimal wavepackets in streamwise corner flow},
    Author = {Schmidt, O. T. and Hosseini, S. M. and Rist, Ulrich and Hanifi, A. and Henningson, D. S.},
    Journal = {Journal of Fluid Mechanics},
    Year = {2015},
    Pages = {405--435},
    Volume = {766},
    Doi = {10.1017/jfm.2015.18},
    File = {:SchmidtEtAl_2015_JFM.pdf:PDF},
    Publisher = {Cambridge Univ Press}
    }