Hamiltonian dynamics of vortex lines in hydrodynamic-type systems
- 1 June 1998
- journal article
- Published by Pleiades Publishing Ltd in JETP Letters
- Vol. 67 (12) , 1076-1081
- https://doi.org/10.1134/1.567795
Abstract
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=∫∣Ω∣dr.Keywords
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