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The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation Full article

Journal Journal of Applied and Industrial Mathematics
ISSN: 1990-4789
Output data Year: 2019, Volume: 13, Number: 3, Pages: 460-471 Pages count : 12 DOI: 10.1134/s1990478919030074
Tags stratified fluid, stationary flow, instability, small perturbation, Taylor–Goldstein equation, Miles Theorem, analytical solution, asymptotic expansion
Authors Gavril’eva A.A. 1 , Gubarev Yu.G. 2,3 , Lebedev M.P. 4
Affiliations
1 Larionov Institute of Physical and Technical Problems of the North, ul. Oktyabr’skaya 1, Yakutsk, 677891 Russia
2 Lavrent’ev Institute of Hydrodynamics, pr. Akad. Lavrent’eva 15, Novosibirsk, 630090 Russia
3 Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
4 Yakutsk Scientific Center, ul. Petrovskogo 2, Yakutsk, 677000 Russia

Funding (2)

1 Министерство науки и высшего образования Российской Федерации FWGG-2021-0008
2 Министерство науки и высшего образования Российской Федерации FWGG-2021-0004

Abstract: We study the problem of the linear stability of stationary plane-parallel shear flows of an inviscid stratified incompressible fluid in the gravity field between two fixed impermeable solid parallel infinite plates with respect to plane perturbations in the Boussinesq approximation and without it. For both cases, we construct some analytical examples of steady plane-parallel shear flows of an ideal density-heterogeneous incompressible fluid and small plane perturbations in the form of normal waves imposed on them, whose asymptotic behavior proves that these perturbations grow in time regardless of whether the well-known result of spectral stability theory (the Miles Theorem) is valid or not.
Cite: Gavril’eva A.A. , Gubarev Y.G. , Lebedev M.P.
The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation
Journal of Applied and Industrial Mathematics. 2019. V.13. N3. P.460-471. DOI: 10.1134/s1990478919030074 Scopus РИНЦ OpenAlex
Dates:
Submitted: Apr 22, 2019
Accepted: Jun 13, 2019
Identifiers:
Scopus: 2-s2.0-85071622115
Elibrary: 41625885
OpenAlex: W2971342713
Citing:
DB Citing
Scopus 16
OpenAlex 19
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