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Hydrodynamical equations for fully relativistic flows at high temperatures are used to investigate the generalized vortex dynamics. Relativistic versions of the Cauchy invariant, Kelvin's Theorem, Weber transformation, Clebsh variables, Ertel's Theorem and the helicity are investigated. Like the nonrelativistic flow, it is shown that the dynamics of the generalized vortex lines is determined by the normal component of the fluid velocity to the vortex line vn. Similar to the nonrelativistic case, the equation for vn is shown to be formally like a new charged fluid but (unlike the nonrelativistic flow) with a new formal thermodynamics. The relativistic incompressibility concept is used to establish its differences from the nonrelativistic treatment.
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