The miles theorem and new particular solutions to the Taylor–Goldstein equation
- Authors: Gavrilieva A.A.1, Gubarev Y.G.2,3, Lebedev M.P.1,4
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Affiliations:
- Larionov Institute of Physical and Technical Problems of the North
- Lavrentyev Institute of Hydrodynamics
- Novosibirsk National Research State University
- Ammosov North-Eastern Federal University
- Issue: Vol 38, No 3 (2017)
- Pages: 560-570
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199476
- DOI: https://doi.org/10.1134/S1995080217030039
- ID: 199476
Cite item
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.
About the authors
A. A. Gavrilieva
Larionov Institute of Physical and Technical Problems of the North
Author for correspondence.
Email: gav-ann@yandex.ru
Russian Federation, Yakutsk, 677891
Yu. G. Gubarev
Lavrentyev Institute of Hydrodynamics; Novosibirsk National Research State University
Email: gav-ann@yandex.ru
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
M. P. Lebedev
Larionov Institute of Physical and Technical Problems of the North; Ammosov North-Eastern Federal University
Email: gav-ann@yandex.ru
Russian Federation, Yakutsk, 677891; Yakutsk, 677000