Hamiltonian description of vortex systems
Mathematical Physics
2020-04-22 v1 math.MP
Abstract
In the framework of 2D ideal Hydrodynamics a vortex system is defined as a smooth vorticity function having few positive local maxima and negative local minima separated by curves of zero vorticity. Invariants of such structures are discussed following from the vorticity conservation law and invertibility of Lagrangian motion. Hamiltonian formalism for vortex systems is developed by introducing new functional variables diagonalizing the original non-canonical Poisson bracket.
Cite
@article{arxiv.1910.11967,
title = {Hamiltonian description of vortex systems},
author = {Leonid I. Piterbarg},
journal= {arXiv preprint arXiv:1910.11967},
year = {2020}
}
Comments
Accepted at "Theoretical and Mathematical Physics", Springer. Will be published in one of the Spring 2020 issues