The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation Full article
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Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 |
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| 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 | ||||||||
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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
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 |