Abstract
In the framework of two-dimensional ideal hydrodynamics, we define a vortex system as a smooth vorticity function with a few local positive maximums and negative minimums separated by curves of zero vorticity. We discuss the invariants of such structures that follow from the vorticity conservation law and the invertibility of Lagrangian motion. Introducing new functional variables diagonalizing the original noncanonical Poisson bracket, we develop a Hamiltonian formalism for vortex systems.
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Acknowledgments
The author is very grateful to G. G. Sutyrin for a useful discussion of the dipole example. Comments of a referee helped to correct numerical results concerning the monopole.
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 202, No. 3, pp. 474-491, March, 2020.
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Piterbarg, L.I. Hamiltonian description of vortex systems. Theor Math Phys 202, 412–427 (2020). https://doi.org/10.1134/S0040577920030137
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DOI: https://doi.org/10.1134/S0040577920030137