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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
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.
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
Linking options:
https://www.mathnet.ru/eng/danma148 https://www.mathnet.ru/eng/danma/v496/p26
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Abstract page: | 107 | Full-text PDF : | 42 | References: | 12 |
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