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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 496, Pages 26–29
DOI: https://doi.org/10.31857/S2686954321010045
(Mi danma148)
 

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Asymptotics of eigenvalues in the Orr–Sommerfeld problem for low velocities of unperturbed flow

D. V. Georgievskiiabcd

a Lomonosov Moscow State University, Moscow, Russian Federation
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russian Federation
c Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation
d World-Class Scientific Center "Supersonic – MSU", Moscow, Russian Federation
Full-text PDF (119 kB) Citations (1)
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Abstract: An asymptotic analysis of the eigenvalues and eigenfunctions in the Orr–Sommerfeld problem is carried out in the case when the velocity of the main plane-parallel shear flow in a layer of a Newtonian viscous fluid is low in a certain measure. The eigenvalues and corresponding eigenfunctions in the layer at rest are used as a zero approximation. For their perturbations, explicit analytical expressions are obtained in the linear approximation. It is shown that, FOR low velocities of the main shear flow, the perturbations of eigenvalues corresponding to monotonic decay near the rest in a viscous layer are such that, regardless of the velocity profile, the decay decrement remains the same, but an oscillatory component appears that is smaller in order by one than this decrement.
Keywords: Orr–Sommerfeld problem, eigenvalue, eigenfunction, flow, viscous fluid, stability, perturbation.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10085 мк
19-01-00016а
This work was supported by the Russian Foundation for Basic Research, grant nos. 18-29-10085mk and 19-01-00016a.
Presented: V. A. Sadovnichii
Received: 26.08.2020
Revised: 27.11.2020
Accepted: 27.11.2020
English version:
Doklady Mathematics, 2021, Volume 103, Issue 1, Pages 19–22
DOI: https://doi.org/10.1134/S106456242101004X
Bibliographic databases:
Document Type: Article
UDC: 532.517.3
Language: Russian
Citation: D. V. Georgievskii, “Asymptotics of eigenvalues in the Orr–Sommerfeld problem for low velocities of unperturbed flow”, Dokl. RAN. Math. Inf. Proc. Upr., 496 (2021), 26–29; Dokl. Math., 103:1 (2021), 19–22
Citation in format AMSBIB
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\by D.~V.~Georgievskii
\paper Asymptotics of eigenvalues in the Orr--Sommerfeld problem for low velocities of unperturbed flow
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 496
\pages 26--29
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\crossref{https://doi.org/10.31857/S2686954321010045}
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\transl
\jour Dokl. Math.
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\vol 103
\issue 1
\pages 19--22
\crossref{https://doi.org/10.1134/S106456242101004X}
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    Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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