Relativistic viscoelastic fluid mechanics
- Department of Physics, Kyoto University, Kyoto 606-8502 (Japan)
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
- OSTI ID:
- 21611553
- Journal Information:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 84, Issue 2; Other Information: DOI: 10.1103/PhysRevE.84.026316; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1539-3755
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
97 MATHEMATICAL METHODS AND COMPUTING
DISTURBANCES
ELASTICITY
ENTROPY
EQUILIBRIUM
FLUID MECHANICS
MINKOWSKI SPACE
NAVIER-STOKES EQUATIONS
RELATIVISTIC RANGE
SYMMETRY
THERMODYNAMICS
WAVE EQUATIONS
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
MATHEMATICAL SPACE
MECHANICAL PROPERTIES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
SPACE
THERMODYNAMIC PROPERTIES