Hamiltonian description of vortex systems

TL;DR

This paper develops a Hamiltonian formalism for vortex systems in 2D ideal hydrodynamics, introducing new variables to diagonalize the Poisson bracket and analyze vortex invariants.

Contribution

It introduces a novel Hamiltonian framework for vortex systems using functional variables that simplify the Poisson structure.

Findings

Hamiltonian formalism for vortex dynamics is established.

New functional variables diagonalize the Poisson bracket.

Invariants of vortex structures are discussed based on vorticity conservation.

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.