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Radiophysics and Quantum Electronics

, Volume 39, Issue 6, pp 518–526 | Cite as

Matrix formulation of hydrodynamics and extension of ptolemaic flows to three-dimensional motions

  • A. A. Abrashkin
  • D. A. Zen'kovich
  • E. I. Yakubovich
Article

Abstract

A new matrix formulation of Lagrange hydrodynamic equations is proposed. Exact solutions of those equations are obtained in matrix form. It is found that precession of vortex lines around some fixed axis in space is a general property of the flows described by those solutions. Two types of fluid motion are studied. Flows of the first type have straight vortex lines, and their particle trajectories are windings on toroidal surfaces. The other flows have plane particle trajectories, and their vortex lines are arbitrarily shaped plane curves. All these motions are shown to be three-dimensional generalizations of plane Ptolemaic flows [1,2].

Keywords

Vortex Exact Solution Matrix Formulation General Property Quantum Electronics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. A. Abrashkin and E. I. Yakubovich, “On Plane Vortex Flows of Ideal Fluid,”Dok. Akad. Nauk SSSR,276, No. 1, 76 (1984).Google Scholar
  2. 2.
    A. A. 'Abrashkin and E. I. Yakubovich, “On Unsteady-state Vortex Flows of Ideal Incompressible Fluid,”Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 57 (1985).Google Scholar
  3. 3.
    P. G. Saffman, “Dynamics of Vorticity,” in:Modern Hydrodynamics. Success and Problems. (G. K. Batchelor and H. K. Moffat, eds.) [Russian translation], Mir, Moscow (1984), p. 77.Google Scholar
  4. 4.
    H. Lamb,Hydrodynamics, Cambridge Univ. Press (1932).Google Scholar
  5. 5.
    G. K. Batchelor,An Introduction to Fluid Dynamics, Cambridge Univ. Press (1967).Google Scholar
  6. 6.
    S. Chandrasekhar,Ellipsoidal Figures of Equilibrium [Russian translation], Mir, Moscow (1973).Google Scholar
  7. 7.
    L. V. Ovsyannikov, “General Equations and Examples” [in Russian], in:Problem on Unsteady Motion of a Fluid with Free Boundary, Nauka (Sibirian Branch), Novosibirsk (1967), p. 5.Google Scholar
  8. 8.
    O. M. Lavrentieva, “On Motion of a Fluid Ellipsoid,”Dokl. Akad. Nauk SSSR,253, No. 4, 828 (1988).Google Scholar
  9. 9.
    A. M. Obukhov, “Three-Mode Mixing in an Incompressible Fluid,”Izv. Vyssh. Uchebn. Zaved., Radiofiz.,19, Nos. 5 and 6, 864 (1976).Google Scholar
  10. 10.
    V. K. Andreev,Stability of Unstable Motions of a Fluid with Free Boundary [in Russian], Nauka (Sibirean Branch), Novosibirsk (1992).Google Scholar
  11. 11.
    N. E. Kochin, I. A. Kibel', and N. V. Roze,Theoretical Hydrodynamics. Part 1 [in Russian], Fizmatgiz, Moscow (1963).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • A. A. Abrashkin
    • 1
    • 2
  • D. A. Zen'kovich
    • 1
    • 2
  • E. I. Yakubovich
    • 1
    • 2
  1. 1.Institute of Applied MechanicsRussian Academy of SciencesMoscow
  2. 2.Institute of Applied PhysicsRussian Academy of SciencesNizhny Novgorod

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