Standard

The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation. / Gavril’eva, A. A.; Gubarev, Yu G.; Lebedev, M. P.

In: Journal of Applied and Industrial Mathematics, Vol. 13, No. 3, 01.07.2019, p. 460-471.

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

Harvard

Gavril’eva, AA, Gubarev, YG & Lebedev, MP 2019, 'The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation', Journal of Applied and Industrial Mathematics, vol. 13, no. 3, pp. 460-471. https://doi.org/10.1134/S1990478919030074

APA

Gavril’eva, A. A., Gubarev, Y. G., & Lebedev, M. P. (2019). The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation. Journal of Applied and Industrial Mathematics, 13(3), 460-471. https://doi.org/10.1134/S1990478919030074

Vancouver

Gavril’eva AA, Gubarev YG, Lebedev MP. The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation. Journal of Applied and Industrial Mathematics. 2019 Jul 1;13(3):460-471. doi: 10.1134/S1990478919030074

Author

Gavril’eva, A. A. ; Gubarev, Yu G. ; Lebedev, M. P. / The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation. In: Journal of Applied and Industrial Mathematics. 2019 ; Vol. 13, No. 3. pp. 460-471.

BibTeX

@article{480b6c8dd08f434988ed45c0e78446d3,
title = "The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation",
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.",
keywords = "analytical solution, asymptotic expansion, instability, Miles Theorem, small perturbation, stationary flow, stratified fluid, Taylor-Goldstein equation",
author = "Gavril{\textquoteright}eva, {A. A.} and Gubarev, {Yu G.} and Lebedev, {M. P.}",
year = "2019",
month = jul,
day = "1",
doi = "10.1134/S1990478919030074",
language = "English",
volume = "13",
pages = "460--471",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "3",

}

RIS

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