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

V. A. Vladimirov, K. I. Ilin

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)425-437
Number of pages13
JournalTheoretical and Computational Fluid Dynamics
Volume10
Issue number1-4
Publication statusPublished - 1998

Fingerprint

incompressible fluids
steady flow
Steady flow
rotational flow
Rotational flow
Fluids
two dimensional flow
body fluids
Body fluids
rigid structures
variational principles
fluids
cross sections
energy

ASJC Scopus subject areas

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

Cite this

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

In: Theoretical and Computational Fluid Dynamics, Vol. 10, No. 1-4, 1998, p. 425-437.

Research output: Contribution to journalArticle

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