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

V. A. Vladimirov, K. I. Ilin

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4 Citations (Scopus)


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
Issue number1-4
Publication statusPublished - 1998


ASJC Scopus subject areas

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

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