Hamiltonian dynamics of vortex lines in hydrodynamic-type systems
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.
- Publication:
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Soviet Journal of Experimental and Theoretical Physics Letters
- Pub Date:
- June 1998
- DOI:
- 10.1134/1.567795
- Bibcode:
- 1998JETPL..67.1076K
- Keywords:
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- 47.32.‑y