Standard

The miles theorem and new particular solutions to the Taylor–Goldstein equation. / Gavrilieva, A. A.; Gubarev, Yu G.; Lebedev, M. P.

In: Lobachevskii Journal of Mathematics, Vol. 38, No. 3, 01.05.2017, p. 560-570.

Research output: Contribution to journal › Article › peer-review

Harvard

Gavrilieva, AA, Gubarev, YG & Lebedev, MP 2017, 'The miles theorem and new particular solutions to the Taylor–Goldstein equation', Lobachevskii Journal of Mathematics, vol. 38, no. 3, pp. 560-570. https://doi.org/10.1134/S1995080217030039

APA

Gavrilieva, A. A., Gubarev, Y. G., & Lebedev, M. P. (2017). The miles theorem and new particular solutions to the Taylor–Goldstein equation. Lobachevskii Journal of Mathematics, 38(3), 560-570. https://doi.org/10.1134/S1995080217030039

Vancouver

Gavrilieva AA, Gubarev YG, Lebedev MP. The miles theorem and new particular solutions to the Taylor–Goldstein equation. Lobachevskii Journal of Mathematics. 2017 May 1;38(3):560-570. doi: 10.1134/S1995080217030039

Author

Gavrilieva, A. A. ; Gubarev, Yu G. ; Lebedev, M. P. / The miles theorem and new particular solutions to the Taylor–Goldstein equation. In: Lobachevskii Journal of Mathematics. 2017 ; Vol. 38, No. 3. pp. 560-570.

BibTeX

@article{12762b31787348348d96d06822e747e0,
title = "The miles theorem and new particular solutions to the Taylor–Goldstein equation",
abstract = "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.",
keywords = "a priori estimate, analytical solutions, Bessel functions, Boussinesq approximation, direct Lyapunov method, ideal stratified fluid, instability, Miles theorem, plane perturbations, stability, steady-state flows, Whittaker functions",
author = "Gavrilieva, {A. A.} and Gubarev, {Yu G.} and Lebedev, {M. P.}",
year = "2017",
month = may,
day = "1",
doi = "10.1134/S1995080217030039",
language = "English",
volume = "38",
pages = "560--570",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "Maik Nauka Publishing / Springer SBM",
number = "3",

}

RIS

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