Vorticity and helicity in relativistic heat-conducting fluid

Abstract

The evolution of heat-conducting fluid described by a pair of Maxwell-like equations is used to construct thermal-fluid helicity and thermal-helicity currents. These currents are found to be dissipative. It is shown that the magnetic part of the particle vorticity two-form is a thermal-fluid vorticity flux vector field composed of a linear combination of the fluid’s vorticity and a spacelike twist of heat flow lines. Heat flow lines are non-geodesic because of the interplay between gravitation and the entropy entrainment in a system composed of a heat-conducting fluid which is in state of rapid differential rotation and far from equilibrium. In general, alignment of the heat flux vector with that of the fluid’s vorticity leads to non-conservation of thermal-fluid vorticity flux in both a thermal-fluid flux tube and a stream tube. It is demonstrated that the twist of the fluid’s vortex lines is caused by the heat flow along the fluid’s vorticity vector in the case of an axisymmetric stationary differentially rotating heat-conducting fluid configuration. In this case, dissipation of thermal-fluid vorticity flux along the flux tube is caused by coupled effects of the fluid’s vorticity magnitude, thermal resistivity and entropy entrainment.