Wednesday, July 10, 2013

1307.2477 (Tomoi Koide et al.)

Bivelocity picture in the nonrelativistic limit of relativistic

Tomoi Koide, Rudnei O. Ramos, Gustavo S. Vicente
We discuss the nonrelativistic limit of relativistic hydrodynamics. The lowest order truncation of the velocity expansion leads to the Navier-Stokes-Fourier theory. However, when the next-to-leading order corrections are included, the equations can be expressed concurrently with two different fluid velocities; one parallel to the conserved charge current flow (which follows the Eckart definition) and the other parallel to the energy current flow (which follows the Landau-Lifshitz definition). We compare this next-to-leading order relativistic hydrodynamics with the bivelocity hydrodynamics, which is one of the generalizations of the Navier-Stokes-Fourier theory and is formulated such as to include the usual mass velocity and also a new velocity, called the volume velocity. We find that the volume velocity can be identified with the velocity obtained in the Landau-Lifshitz definition. Thus, various assumptions that are introduced in the formulation of the bivelocity hydrodynamics are shown to be reproduced in the next-to-leading order relativistic hydrodynamics.
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