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A covariant action principle for dissipative fluid dynamics: from formalism to fundamental physics

A covariant action principle for dissipative fluid dynamics: from formalism to fundamental physics
A covariant action principle for dissipative fluid dynamics: from formalism to fundamental physics
We present a new variational framework for dissipative general relativistic fluid dynamics. The model extends the convective variational principle for multi-fluid systems to account for a range of dissipation channels. The key ingredients in the construction are (i) the use of a lower dimensional matter space for each fluid component, and (ii) an extended functional dependence for the associated volume forms. In an effort to make the concepts clear, the formalism is developed step-by-step with model examples considered at each level. Thus we consider a model for heat flow, derive the relativistic Navier-Stokes equations and discuss why the individual dissipative stress tensors need not be spacetime symmetric. We argue that the new formalism, which notably does not involve an expansion away from an assumed equilibrium state, provides a conceptual breakthrough in this area of research. We also provide an ambitious list of directions in which one may want to extend it in the future. This involves an exciting set of problems, relating to both applications and foundational issues.
0264-9381
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Comer, G.L.
f2c1746c-8638-4268-94f0-e5d4375f0358
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Comer, G.L.
f2c1746c-8638-4268-94f0-e5d4375f0358

Andersson, N. and Comer, G.L. (2015) A covariant action principle for dissipative fluid dynamics: from formalism to fundamental physics. Classical and Quantum Gravity, 32 (7). (doi:10.1088/0264-9381/32/7/075008).

Record type: Article

Abstract

We present a new variational framework for dissipative general relativistic fluid dynamics. The model extends the convective variational principle for multi-fluid systems to account for a range of dissipation channels. The key ingredients in the construction are (i) the use of a lower dimensional matter space for each fluid component, and (ii) an extended functional dependence for the associated volume forms. In an effort to make the concepts clear, the formalism is developed step-by-step with model examples considered at each level. Thus we consider a model for heat flow, derive the relativistic Navier-Stokes equations and discuss why the individual dissipative stress tensors need not be spacetime symmetric. We argue that the new formalism, which notably does not involve an expansion away from an assumed equilibrium state, provides a conceptual breakthrough in this area of research. We also provide an ambitious list of directions in which one may want to extend it in the future. This involves an exciting set of problems, relating to both applications and foundational issues.

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Accepted/In Press date: 9 January 2015
Published date: 13 March 2015
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 410565
URI: https://eprints.soton.ac.uk/id/eprint/410565
ISSN: 0264-9381
PURE UUID: 0886c70a-e87b-43a1-b652-47879cc7306f
ORCID for N. Andersson: ORCID iD orcid.org/0000-0001-8550-3843

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Date deposited: 09 Jun 2017 09:08
Last modified: 18 May 2019 00:37

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