Formulating viscous hydrodynamics for large velocity gradients

Journal Article · Fri Feb 15 04:00:00 EST 2008 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PHYSREVC.77.024910· OSTI ID:21068146

Pratt, Scott ^[1]

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1. Department of Physics and Astronomy, Michigan State University East Lansing, Michigan 48824-1321 (United States)

Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity gradients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, which treat the spatial components of the stress-energy tensor {tau}{sub ij} as dynamical objects, introduce new parameters, such as the relaxation times describing nonequilibrium behavior of the elements {tau}{sub ij}. By considering linear response theory and entropy constraints, we show how the additional parameters are related to fluctuations of {tau}{sub ij}. Furthermore, the Israel-Stewart parameters are analyzed for their ability to provide stable and physical solutions for sound waves. Finally, it is shown how these parameters, which are naturally described by correlation functions in real time, might be constrained by lattice calculations, which are based on path-integral formulations in imaginary time.

• OSTI ID: 21068146
• Journal Information: Physical Review. C, Nuclear Physics, Journal Name: Physical Review. C, Nuclear Physics Journal Issue: 2 Vol. 77; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRECTIONS
CORRELATION FUNCTIONS
ENTROPY
FLUCTUATIONS
HEAVY ION REACTIONS
HYDRODYNAMIC MODEL
HYDRODYNAMICS
MATHEMATICAL SOLUTIONS
NAVIER-STOKES EQUATIONS
PATH INTEGRALS
RELATIVISTIC RANGE
RELAXATION
SOUND WAVES
STRESSES
TENSORS
VELOCITY