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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 1, Pages 164–187 (Mi zvmmf4818)  

This article is cited in 2 scientific papers (total in 2 papers)

Dispersion equations in the problem of the stability of transonic flows and some of their properties

V. I. Zhuk, A. V. Chernyshev

Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: For the Navier-Stokes equations, asymptotic simplifying techniques are discussed aimed at the description of unsteady boundary-layer processes associated with the formation of instability. The form of the asymptotic series is based on the triple-deck treatment of solutions to boundary value problems (viscous-inviscid interaction). Although most attention is focused on transonic outer flows, a comparative analysis with the asymptotic theory of boundary layer stability in subsonic flows is given. The parameters of internal waves near the lower and upper branches of the neutral curve are associated with different structures of the perturbation field. These parameters satisfy dispersion relations derived by solving eigenvalue problems. The dispersion relations are investigated in complex planes.

Key words: triple-deck theory of viscous-inviscid interaction, boundary layer, transonic and subsonic flows, stability, dispersion relation, Airy function, Tollmien-Schlichting wave, spectrum of eigenmodes, increment of growth, phase velocity, wave number, neutral stability curve.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:1, 157–179

Bibliographic databases:

UDC: 519.634
Received: 11.01.2009

Citation: V. I. Zhuk, A. V. Chernyshev, “Dispersion equations in the problem of the stability of transonic flows and some of their properties”, Zh. Vychisl. Mat. Mat. Fiz., 50:1 (2010), 164–187; Comput. Math. Math. Phys., 50:1 (2010), 157–179

Citation in format AMSBIB
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\paper Dispersion equations in the problem of the stability of transonic flows and some of their properties
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\pages 164--187
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\pages 157--179
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Bogdanov, V. N. Diesperov, V. I. Zhuk, A. V. Chernyshev, “Triple-deck theory in transonic flows and boundary layer stability”, Comput. Math. Math. Phys., 50:12 (2010), 2095–2108  mathnet  crossref  adsnasa
    2. V. I. Zhuk, “Asymptotic approach to the problem of boundary layer instability in transonic flow”, Comput. Math. Math. Phys., 58:3 (2018), 410–424  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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