### Abstract

We study the stability of a rigid body in a steady rotational flow of an inviscid incompressible fluid. We consider the two-dimensional problem: a body is an infinite cylinder with arbitrary cross section moving perpendicularly to its axis, a flow is two-dimensional, i.e., it does not depend on the coordinate along the axis of a cylinder; both body and fluid are in a two-dimensional bounded domain with an arbitrary smooth boundary. Arnold's method is exploited to obtain sufficient conditions for linear stability of an equilibrium of a body in a steady rotational flow. We first establish a new energy-type variational principle which is a natural generalization of the well-known Arnold's result (1965a, 1966) to the system "body + fluid." Then, by Arnold's technique, a general sufficient condition for linear stability is obtained.

Original language | English |
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Pages (from-to) | 425-437 |

Number of pages | 13 |

Journal | Theoretical and Computational Fluid Dynamics |

Volume | 10 |

Issue number | 1-4 |

Publication status | Published - 1998 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Theoretical and Computational Fluid Dynamics*,

*10*(1-4), 425-437.

**On the arnold stability of a solid in a plane steady flow of an ideal incompressible fluid.** / Vladimirov, V. A.; Ilin, K. I.

Research output: Contribution to journal › Article

*Theoretical and Computational Fluid Dynamics*, vol. 10, no. 1-4, pp. 425-437.

}

TY - JOUR

T1 - On the arnold stability of a solid in a plane steady flow of an ideal incompressible fluid

AU - Vladimirov, V. A.

AU - Ilin, K. I.

PY - 1998

Y1 - 1998

N2 - We study the stability of a rigid body in a steady rotational flow of an inviscid incompressible fluid. We consider the two-dimensional problem: a body is an infinite cylinder with arbitrary cross section moving perpendicularly to its axis, a flow is two-dimensional, i.e., it does not depend on the coordinate along the axis of a cylinder; both body and fluid are in a two-dimensional bounded domain with an arbitrary smooth boundary. Arnold's method is exploited to obtain sufficient conditions for linear stability of an equilibrium of a body in a steady rotational flow. We first establish a new energy-type variational principle which is a natural generalization of the well-known Arnold's result (1965a, 1966) to the system "body + fluid." Then, by Arnold's technique, a general sufficient condition for linear stability is obtained.

AB - We study the stability of a rigid body in a steady rotational flow of an inviscid incompressible fluid. We consider the two-dimensional problem: a body is an infinite cylinder with arbitrary cross section moving perpendicularly to its axis, a flow is two-dimensional, i.e., it does not depend on the coordinate along the axis of a cylinder; both body and fluid are in a two-dimensional bounded domain with an arbitrary smooth boundary. Arnold's method is exploited to obtain sufficient conditions for linear stability of an equilibrium of a body in a steady rotational flow. We first establish a new energy-type variational principle which is a natural generalization of the well-known Arnold's result (1965a, 1966) to the system "body + fluid." Then, by Arnold's technique, a general sufficient condition for linear stability is obtained.

UR - http://www.scopus.com/inward/record.url?scp=0041179396&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041179396&partnerID=8YFLogxK

M3 - Article

VL - 10

SP - 425

EP - 437

JO - Theoretical and Computational Fluid Dynamics

JF - Theoretical and Computational Fluid Dynamics

SN - 0935-4964

IS - 1-4

ER -