Hamiltonian dynamics of vortex lines in hydrodynamic-type systems

  • E. A. Kuznetsov
  • V. P. Ruban
Methods Of Theoretical Physics


It is shown that the degeneracy of the noncanonical Poisson bracket operating on the space of solenoidal vector fields that arises due to the freezing-in of the curl of the velocity [E. A. Kuznetsov and A. V. Mikhailov, Phys. Lett. A 77, 37 (1980)] is lifted when the vorticity Ω is represented in terms of vortex lines. This representation makes it possible to integrate the equation of motion of the vorticity for a system with the Hamiltonian H=∫∣Ωdr.

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Copyright information

© MAIK "Nauka/Interperiodica" 1998

Authors and Affiliations

  • E. A. Kuznetsov
    • 1
  • V. P. Ruban
    • 1
  1. 1.L. D. Landau Institute of Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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