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The miles theorem and new particular solutions to the Taylor–Goldstein equation. / Gavrilieva, A. A.; Gubarev, Yu G.; Lebedev, M. P.
в: Lobachevskii Journal of Mathematics, Том 38, № 3, 01.05.2017, стр. 560-570.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - The miles theorem and new particular solutions to the Taylor–Goldstein equation
AU - Gavrilieva, A. A.
AU - Gubarev, Yu G.
AU - Lebedev, M. P.
PY - 2017/5/1
Y1 - 2017/5/1
N2 - The direct Lyapunov method is used to prove the absolute linear instability of steadystate plane-parallel shear flows of an inviscid stratified incompressible fluid in the gravity field with respect to plane perturbations both in the Boussinesq and non-Boussinesq approximations. A strict description is given for the applicability of the known necessary condition for linear instability of steady-state plane-parallel shear flows of an ideal nonuniform (by density) incompressible fluid in the gravity field both in the Boussinesq and non-Boussinesq approximations (the Miles theorem). Analytical examples of illustrative character are constructed.
AB - The direct Lyapunov method is used to prove the absolute linear instability of steadystate plane-parallel shear flows of an inviscid stratified incompressible fluid in the gravity field with respect to plane perturbations both in the Boussinesq and non-Boussinesq approximations. A strict description is given for the applicability of the known necessary condition for linear instability of steady-state plane-parallel shear flows of an ideal nonuniform (by density) incompressible fluid in the gravity field both in the Boussinesq and non-Boussinesq approximations (the Miles theorem). Analytical examples of illustrative character are constructed.
KW - a priori estimate
KW - analytical solutions
KW - Bessel functions
KW - Boussinesq approximation
KW - direct Lyapunov method
KW - ideal stratified fluid
KW - instability
KW - Miles theorem
KW - plane perturbations
KW - stability
KW - steady-state flows
KW - Whittaker functions
UR - http://www.scopus.com/inward/record.url?scp=85019681323&partnerID=8YFLogxK
U2 - 10.1134/S1995080217030039
DO - 10.1134/S1995080217030039
M3 - Article
AN - SCOPUS:85019681323
VL - 38
SP - 560
EP - 570
JO - Lobachevskii Journal of Mathematics
JF - Lobachevskii Journal of Mathematics
SN - 1995-0802
IS - 3
ER -
ID: 10190982