Three-dimensional instability of an elliptic Kirchhoff vortex

V. A. Vladimirov, K. I. Il'in

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The instability of a Kirchhoff vortex [1-3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4-6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4-9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.

Original languageEnglish
Pages (from-to)356-360
Number of pages5
JournalFluid Dynamics
Volume23
Issue number3
DOIs
Publication statusPublished - May 1988

Fingerprint

Vortex flow
eccentricity
vortices
approximation
perturbation
vessels
cross sections

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

Cite this

Three-dimensional instability of an elliptic Kirchhoff vortex. / Vladimirov, V. A.; Il'in, K. I.

In: Fluid Dynamics, Vol. 23, No. 3, 05.1988, p. 356-360.

Research output: Contribution to journalArticle

@article{589f8552b42f46b7ad747efbda550a01,
title = "Three-dimensional instability of an elliptic Kirchhoff vortex",
abstract = "The instability of a Kirchhoff vortex [1-3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4-6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4-9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.",
author = "Vladimirov, {V. A.} and Il'in, {K. I.}",
year = "1988",
month = "5",
doi = "10.1007/BF01054740",
language = "English",
volume = "23",
pages = "356--360",
journal = "Fluid Dynamics",
issn = "0015-4628",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "3",

}

TY - JOUR

T1 - Three-dimensional instability of an elliptic Kirchhoff vortex

AU - Vladimirov, V. A.

AU - Il'in, K. I.

PY - 1988/5

Y1 - 1988/5

N2 - The instability of a Kirchhoff vortex [1-3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4-6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4-9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.

AB - The instability of a Kirchhoff vortex [1-3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4-6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4-9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.

UR - http://www.scopus.com/inward/record.url?scp=0024113006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024113006&partnerID=8YFLogxK

U2 - 10.1007/BF01054740

DO - 10.1007/BF01054740

M3 - Article

VL - 23

SP - 356

EP - 360

JO - Fluid Dynamics

JF - Fluid Dynamics

SN - 0015-4628

IS - 3

ER -