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Nelin. Dinam., 2014, Volume 10, Number 3, Pages 345–354 (Mi nd448)  

This article is cited in 2 scientific papers (total in 2 papers)

Evolution of three-dimensional picture of disturbances imposed on a rotational-axial flow in a cylindrical clearance

Dmitrii V. Georgievskii

Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia

Abstract: This work deals with stability relative to three-dimensional disturbances of a compound rotational-axial shear flow of Newtonian viscous fluid inside a cylindrical clearance. The corresponding linearized problem on stability is stated with the sticking conditions. On the basis of the integral relation method permitting to obtain sufficient estimates of stability as well as lower estimates for critical Reynolds numbers, the general upper estimate of real part of a spectral parameter (responding to stability) is derived. This estimate is defined more exactly for cases of both three-dimensional axially symmetric disturbances and two-dimensional non-axially symmetric ones.

Keywords: Newtonian fluid, cylindrical clearance, shear flow, rotation, the integral relation method, quadratic functional, variational inequality, stability, critical Reynolds number.

Full text: PDF file (309 kB)
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Document Type: Article
UDC: 532.516
MSC: 76D05
Received: 21.08.2014
Revised: 24.09.2014

Citation: Dmitrii V. Georgievskii, “Evolution of three-dimensional picture of disturbances imposed on a rotational-axial flow in a cylindrical clearance”, Nelin. Dinam., 10:3 (2014), 345–354

Citation in format AMSBIB
\Bibitem{Geo14}
\by Dmitrii~V.~Georgievskii
\paper Evolution of three-dimensional picture of disturbances imposed on~a~rotational-axial flow in a cylindrical clearance
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 3
\pages 345--354
\mathnet{http://mi.mathnet.ru/nd448}


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    This publication is cited in the following articles:
    1. D. V. Georgievskii, V. G. Putkaradze, G. S. Tlyustangelov, “Three-dimensional perturbations of the radial-rotational spread-sink of a viscous cylindrical layer”, Dokl. Phys., 62:4 (2017), 218–221  crossref  mathscinet  isi  scopus
    2. D. V. Georgievskii, G. S. Tlyustangelov, “Exponential estimates of perturbations of rigid-plastic spreading-sink of an annulus”, Mech. Sol., 52:4 (2017), 465–472  crossref  isi  scopus
  • Нелинейная динамика
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