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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 12, Pages 2208–2222 (Mi zvmmf4984)  

This article is cited in 3 scientific papers (total in 3 papers)

Triple-deck theory in transonic flows and boundary layer stability

A. N. Bogdanov, V. N. Diesperov, V. I. Zhuk, A. V. Chernyshev

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

Abstract: An analysis of the lower branch of the neutral curve for the Blasius boundary layer leads to a perturbed velocity field with a triple-deck structure, which is a rather unexpected result. It is the asymptotic treatment of the stability problem that has a rational basis, since it is in the limit of high Reynolds numbers that the basic flow has the form of a boundary layer. The principles for constructing a boundary layer stability theory based on the triple-deck theory are proposed. 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 branch of the neutral curve are associated with a certain perturbation field pattern. These parameters satisfy dispersion relations derived by solving eigenvalue problems. The dispersion relations are investigated in complex planes.

Key words: triple-deck theory, boundary layer, transonic and subsonic flows, stability, dispersion relation, Airy function, Tollmien–Schlichting wave, spectrum of eigenmodes, increment of growth, phase velocity, wave number, singular parameter.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:12, 2095–2108

Bibliographic databases:

UDC: 519.634
Received: 31.05.2010

Citation: A. N. Bogdanov, V. N. Diesperov, V. I. Zhuk, A. V. Chernyshev, “Triple-deck theory in transonic flows and boundary layer stability”, Zh. Vychisl. Mat. Mat. Fiz., 50:12 (2010), 2208–2222; Comput. Math. Math. Phys., 50:12 (2010), 2095–2108

Citation in format AMSBIB
\by A.~N.~Bogdanov, V.~N.~Diesperov, V.~I.~Zhuk, A.~V.~Chernyshev
\paper Triple-deck theory in transonic flows and boundary layer stability
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2010
\vol 50
\issue 12
\pages 2208--2222
\jour Comput. Math. Math. Phys.
\yr 2010
\vol 50
\issue 12
\pages 2095--2108

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    This publication is cited in the following articles:
    1. Ruban A.I., Bernots T., Kravtsova M.A., “Linear and Nonlinear Receptivity of the Boundary Layer in Transonic Flows”, J. Fluid Mech., 786 (2016)  crossref  mathscinet  zmath  isi  scopus
    2. Bogdanov A.N., Diyesperov V.N., Zhuk V.I., “Asymptotics of Dispersion Curves in Time-Dependent Problems of Free Viscous-Inviscid Interaction At Transonic Speeds”, Dokl. Phys., 62:7 (2017), 350–352  crossref  mathscinet  isi  scopus
    3. Zhuk V.I., “Periodic and Soliton Solutions of An Integral-Differential Equation in the Theory of Transonic Flows With Free Interaction”, Fluid Dyn., 53:2 (2018), 64–73  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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