Linearised dynamics and non-modal instability analysis of an impinging under-expanded supersonic jet

Shahram Karami, Paul C. Stegeman, Vassilis Theofilis, Peter J. Schmid, Julio Soria

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15 Citations (Scopus)


Non-modal instability analysis of the shear layer near the nozzle of a supersonic under-expanded impinging jet is studied. The shear layer instability is considered to be one of the main components of the feedback loop in supersonic jets. The feedback loop is observed in instantaneous visualisations of the density field where it is noted that acoustic waves scattered by the nozzle lip internalise as shear layer instabilities. A modal analysis describes the asymptotic limit of the instability disturbances and fails to capture short-time responses. Therefore, a non-modal analysis which allows the quantitative description of the short-time amplification or decay of a disturbance is performed by means of a local far-field pressure pulse. An impulse response analysis is performed which allows a wide range of frequencies to be excited. The temporal and spatial growths of the disturbances in the shear layer near the nozzle are studied by decomposing the response using dynamic mode decomposition and Hilbert transform analysis. The short-time response shows that disturbances with non-dimensionalised temporal frequencies in the range of 1 to 4 have positive growth rates in the shear layer. The Hilbert transform analysis shows that high non-dimensionalised temporal frequencies (>4) are dampened immediately, whereas low non-dimensionalised temporal frequencies (<1) are neutral. Both dynamic mode decomposition and Hilbert transform analysis show that spatial frequencies between 1 and 3 have positive spatial growth rates. Finally, the envelope of the streamwise velocity disturbances reveals the presence of a convective instability.

Original languageEnglish
Title of host publicationJournal of Physics
Subtitle of host publicationConference Series
EditorsJavier Jiménez
Place of PublicationBristol UK
PublisherIOP Publishing
Number of pages13
Publication statusPublished - 12 Apr 2018
EventMadrid Summer School on Turbulence 2017 - Universidad Politécnica de Madrid, Madrid, Spain
Duration: 29 May 201730 Jun 2017
Conference number: 3rd (Proceedings) (Proceedings) (Proceedings)

Publication series

NameJournal of Physics: Conference Series
PublisherIOP Publishing
ISSN (Print)1742-6588
ISSN (Electronic)1742-6596


ConferenceMadrid Summer School on Turbulence 2017
Internet address


  • Supersonic jet
  • Large-eddy simulation
  • Linearised dynamics

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