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Bivelocity Picture in the Nonrelativistic Limit of Relativistic Hydrodynamics

  • General and Applied Physics
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Abstract

We discuss the nonrelativistic limit of the relativistic Navier-Fourier-Stokes (NFS) theory. The next-to-leading order relativistic corrections to the NFS theory for the Landau-Lifshitz fluid are obtained. While the lowest order truncation of the velocity expansion leads to the usual NFS equations of nonrelativistic fluids, we show that when the next-to-leading order relativistic corrections are included, the equations can be expressed concurrently with two different fluid velocities. One of the fluid velocities is parallel to the conserved charge current (which follows the Eckart definition) and the other one is parallel to the energy current (which follows the Landau-Lifshitz definition). We compare this next-to-leading order relativistic hydrodynamics with bivelocity hydrodynamics, which is one of the generalizations of the NFS theory and is formulated in such a way 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. Then, the structure of bivelocity hydrodynamics, which is derived using various nontrivial assumptions, is reproduced in the NFS theory including the next-to-leading order relativistic corrections.

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Notes

  1. However, the complexity of the generic stability of these theories led some authors to reconsider first-order theories in order to establish this property properly [2–8].

  2. It is well known that higher-order kinetic corrections to the NFS theory leads to the Burnett and super-Burnett equations [38]. The relation between these kinetic corrections and the bivelocity picture was discussed in Refs. [24, 25].

  3. The time scale of the evolution of non-conserved quantities are considered to be short and these are usually not included as hydrodynamic variables.

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Acknowledgments

T. K. acknowledge discussions with G. S. Denicol, X. Huang, and L. S. García-Colinin in the initial stages of the present study and financial support from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). R.O.R. is partially supported by research grants from CNPq and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ). G. S. V. is supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).

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Authors and Affiliations

  1. Instituto de Física, Universidade Federal do Rio de Janeiro, 68528, 21945-970, Rio de Janeiro, Brazil

    Tomoi Koide

  2. Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, 20550-013, Rio de Janeiro, RJ, Brazil

    Rudnei O. Ramos & Gustavo S. Vicente

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  1. Tomoi Koide
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  2. Rudnei O. Ramos
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  3. Gustavo S. Vicente
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Correspondence to Rudnei O. Ramos.

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Koide, T., Ramos, R.O. & Vicente, G.S. Bivelocity Picture in the Nonrelativistic Limit of Relativistic Hydrodynamics. Braz J Phys 45, 102–111 (2015). https://doi.org/10.1007/s13538-014-0288-5

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