Geodesic
Hamiltonian description of vortex systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 474-491

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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.
Mots-clés : vortex, Poisson bracket
Keywords: continuum Hamiltonian system, vorticity, two-dimensional hydrodynamics. 
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     author = {L. I. Piterbarg},
     title = {Hamiltonian description of vortex systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {474--491},
     publisher = {mathdoc},
     volume = {202},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a12/}
}
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L. I. Piterbarg. Hamiltonian description of vortex systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 474-491. http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a12/