Instability of steady flows with constant vorticity in vessels of elliptic cross-section

V. A. Vladimirov, D. G. Vostretsov

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The problem of the stability of steady flows of a perfect incompressible fluid in vessels of elliptic cross-section is studied. The flow velocity field of the main stream is a linear function of the coordinates and the vorticity is constant. The spectral problem for the linear perturbations is solved using the mehtod of consecutive approximations. The instability of the flows to a first approximation is demonstrated. A special case of the flow in a triaxial ellipsoid is analysed in detail. Theoretical predictions agree well with the experimental results /1/. The present paper, unlike the analysis carried out in /1/, deals with an appreciably wider class of perturbations and the Galerkin method of rough a priori approximation is not used. The problem of stability of flows of this type is of interest when describing the properties of a liquid-filled gyroscope /2-4/ and the behaviour of the star and planetary cores /5/. At the same time, a flow with a linear velocity field represents the simplest example of the realization of the new mechanism of instability of rotational flows connected with disturbance of the rotational symmetry /6-9/.

Original languageEnglish
Pages (from-to)279-285
Number of pages7
JournalJournal of Applied Mathematics and Mechanics
Volume50
Issue number3
DOIs
Publication statusPublished - 1986

Fingerprint

Steady flow
Steady Flow
Vorticity
Vessel
Cross section
Velocity Field
Rotational flow
Approximation
Gyroscopes
Perturbation
Galerkin methods
Flow velocity
Rotational symmetry
Perfect Fluid
Gyroscope
Stars
Spectral Problem
Ellipsoid
Galerkin Method
Incompressible Fluid

ASJC Scopus subject areas

  • Mechanical Engineering
  • Applied Mathematics
  • Mathematical Physics
  • Modelling and Simulation

Cite this

Instability of steady flows with constant vorticity in vessels of elliptic cross-section. / Vladimirov, V. A.; Vostretsov, D. G.

In: Journal of Applied Mathematics and Mechanics, Vol. 50, No. 3, 1986, p. 279-285.

Research output: Contribution to journalArticle

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AB - The problem of the stability of steady flows of a perfect incompressible fluid in vessels of elliptic cross-section is studied. The flow velocity field of the main stream is a linear function of the coordinates and the vorticity is constant. The spectral problem for the linear perturbations is solved using the mehtod of consecutive approximations. The instability of the flows to a first approximation is demonstrated. A special case of the flow in a triaxial ellipsoid is analysed in detail. Theoretical predictions agree well with the experimental results /1/. The present paper, unlike the analysis carried out in /1/, deals with an appreciably wider class of perturbations and the Galerkin method of rough a priori approximation is not used. The problem of stability of flows of this type is of interest when describing the properties of a liquid-filled gyroscope /2-4/ and the behaviour of the star and planetary cores /5/. At the same time, a flow with a linear velocity field represents the simplest example of the realization of the new mechanism of instability of rotational flows connected with disturbance of the rotational symmetry /6-9/.

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