Helicity and vortex generation

In this work we have considered the 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. We have studied the evolution of helicity and circulation from the Maxwell-type formulation for compressive fluid equations, 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.