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The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation. / Gavril’eva, A. A.; Gubarev, Yu G.; Lebedev, M. P.
в: Journal of Applied and Industrial Mathematics, Том 13, № 3, 01.07.2019, стр. 460-471.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation
AU - Gavril’eva, A. A.
AU - Gubarev, Yu G.
AU - Lebedev, M. P.
PY - 2019/7/1
Y1 - 2019/7/1
N2 - 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.
AB - 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.
KW - analytical solution
KW - asymptotic expansion
KW - instability
KW - Miles Theorem
KW - small perturbation
KW - stationary flow
KW - stratified fluid
KW - Taylor-Goldstein equation
UR - http://www.scopus.com/inward/record.url?scp=85071622115&partnerID=8YFLogxK
U2 - 10.1134/S1990478919030074
DO - 10.1134/S1990478919030074
M3 - Article
AN - SCOPUS:85071622115
VL - 13
SP - 460
EP - 471
JO - Journal of Applied and Industrial Mathematics
JF - Journal of Applied and Industrial Mathematics
SN - 1990-4789
IS - 3
ER -
ID: 21472881