Helicity and Vortex generation

TL;DR

This paper explores the dynamics of helicity and vortex generation in charged fluids interacting with electromagnetic fields, deriving wave equations and analyzing how electromagnetic effects influence fluid circulation and helicity evolution.

Contribution

It extends the minimal coupling framework to derive Navier-Stokes equations for charged fluids in electromagnetic fields and analyzes wave features and gauge choices affecting vortex dynamics.

Findings

Electromagnetic fields influence vortex and helicity evolution.

Wave equations for velocity and vorticity are derived.

Electromagnetic effects can act as sources for circulation.

Abstract

In this paper we have continued the calculations made recently concerning he generalization of the minimal coupling prescription. We have obtained the Navier-Stokes equation for the charged fluid embedded into an electromagnetic field. We have analyzed the wave feature of the fields. Wave equations for velocity and vorticity were obtained and gauge choices were discussed. In this paper we have studied the evolution of helicity and circulation from the Maxwell type formulation to the equations of a compressible fluid, charged in interaction with an electromagnetic field. We see that for both helicity and circulation there are terms that, in principle, can be considered as source terms or creation of circulation in the dynamics of fluids