Vorticity and magnetic field production in relativistic ideal fluids

TL;DR

This paper investigates how vorticity and magnetic fields can be generated in relativistic ideal fluids, highlighting mechanisms involving entropy and charge density gradients, especially in charged and multi-charged fluids relevant to plasmas and the early universe.

Contribution

It introduces new mechanisms for vorticity and magnetic field production in relativistic fluids involving entropy and charge density inhomogeneities.

Findings

Vorticity in uncharged fluids obeys Kelvin's theorem and is conserved.

Charged fluids can generate vorticity and magnetic fields through entropy and charge density gradients.

Multi-charged fluids produce vorticity even with homogeneous entropy, due to charge density inhomogeneities.

Abstract

In the framework of relativistic ideal hydrodynamics, we study the production mechanism for vorticity and magnetic field in relativistic ideal fluids. It is demonstrated that in the uncharged fluids the thermal vorticity will always satisfy the Kelvin's theorem and the circulation must be conserved. However, in the charged fluids, the vorticity and magnetic field can be produced by the interaction between the entropy gradients and the fluid velocity gradients. Especially, in the multiple charged fluids, the vorticity and magnetic field can be produced by the interaction between the inhomogenous charge density ratio and the fluid velocity gradients even if the entropy distribution is homogeneous, which provides another mechanism for the production of vorticity and magnetic field in relativistic plasmas or in the early universe.