Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 3, Pages 431–446 (Mi zvmmf10694)  

Asymptotic approach to the problem of boundary layer instability in transonic flow

V. I. Zhuk

Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia

Abstract: Tollmien–Schlichting waves can be analyzed using the Prandtl equations involving selfinduced pressure. This circumstance was used as a starting point to examine the properties of the dispersion relation and the eigenmode spectrum, which includes modes with amplitudes increasing with time. The fact that the asymptotic equations for a nonclassical boundary layer (near the lower branch of the neutral curve) have unstable fluctuation solutions is well known in the case of subsonic and transonic flows. At the same time, similar solutions for supersonic external flows do not contain unstable modes. The bifurcation pattern of the behavior of dispersion curves in complex domains gives a mathematical explanation of the sharp change in the stability properties occurring in the transonic range.

Key words: free interaction, boundary layer, transonic and subsonic flow, stability, dispersion relation, Airy function, Tollmien–Schlichting wave, spectrum of eigenmodes, increment of growth, phase velocity, wave number, neutral curve.

DOI: https://doi.org/10.7868/S0044466918030109

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:3, 410–424

Bibliographic databases:

UDC: 519.635
Received: 19.01.2017

Citation: V. I. Zhuk, “Asymptotic approach to the problem of boundary layer instability in transonic flow”, Zh. Vychisl. Mat. Mat. Fiz., 58:3 (2018), 431–446; Comput. Math. Math. Phys., 58:3 (2018), 410–424

Citation in format AMSBIB
\Bibitem{Zhu18}
\by V.~I.~Zhuk
\paper Asymptotic approach to the problem of boundary layer instability in transonic flow
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 3
\pages 431--446
\mathnet{http://mi.mathnet.ru/zvmmf10694}
\crossref{https://doi.org/10.7868/S0044466918030109}
\elib{https://elibrary.ru/item.asp?id=32615746}
\transl
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 3
\pages 410--424
\crossref{https://doi.org/10.1134/S0965542518030156}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000430012700010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045381438}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10694
  • http://mi.mathnet.ru/eng/zvmmf/v58/i3/p431

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:114
    References:19

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021