On linear stability of shear flows of an ideal stratified fluid: Research methods and new results

A. A. Gavrilieva, Yu G. Gubarev

Результат исследования: Научные публикации в периодических изданияхстатья по материалам конференции

Аннотация

The results, that obtained by the spectral method with use of integral relations for the problem of linear stability of steady-state shear plane-parallel flows of an inviscid stratified incompressible fluid in the gravity field with respect to plane perturbations in the Boussinesq approximation and without it, are specified, complemented and developed by the most powerful analytical method of the modern mathematical theory of hydrodynamic stability-the second (or direct) Lyapunov method. In both case, the new analytical method made it possible to prove that given steady-state flows of stratified fluid are absolutely unstable in theoretical sense with respect to small plane perturbations and to obtain the sufficient conditions for practical linear instability of considered flows. The illustrative analytical examples of given steady-state flows and small plane perturbations as normal waves imposed on them are constructed. Using the asymptotic method, it is proved that constructed perturbations grow in time irrespective of the fact whether the Miles-Howard and the Miles-type theorems are valid or not.

Язык оригиналаанглийский
Номер статьи012006
ЖурналJournal of Physics: Conference Series
Том1392
Номер выпуска1
DOI
СостояниеОпубликовано - 13 дек 2019
Событие4th International Conference on Supercomputer Technologies of Mathematical Modelling, SCTeMM 2019 - Moscow, Российская Федерация
Продолжительность: 19 июн 201921 июн 2019

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