The system of three vortexes of two dimensional ideal hydrodinamics as a new example of the (integrable) Nambu- Poisson mechanics

TL;DR

This paper presents a Nambu-Poisson formulation for the three-vortex system in 2D ideal hydrodynamics, demonstrating its integrability through quadratures and providing a new example of Nambu-Poisson mechanics.

Contribution

It introduces a Nambu-Poisson framework for the three-vortex system, showing its integrability and expanding the applications of Nambu mechanics in fluid dynamics.

Findings

The three-vortex system is integrable via quadratures.

A Nambu-Poisson structure is formulated for the vortex dynamics.

The approach offers a new example of Nambu-Poisson mechanics.

Abstract

A Nambu-Poisson formulation of the system of three ordinary differential equations describing dynamics of three vortexes of the ideal two-dimensional hydrodynamics is given. The system is integrated by quadratures.