Formulating viscous hydrodynamics for large velocity gradients

2007/11/25 by Scott Pratt · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Cauchy stress tensor #Classical mechanics #Computational Fluid Dynamics and Aerodynamics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Geometry #High-Energy Particle Collisions Research #Mathematical analysis #Mathematical physics #Mathematics #Non-equilibrium thermodynamics #Path integral formulation #Physics #Quantum mechanics #Relaxation (psychology) #Statistical physics #Tensor (intrinsic definition) #nucl-th

paper · pdf · doi:10.1103/physrevc.77.024910

published as Phys.Rev.C77:024910,2008 · 16 pages

arxiv created 2007/11/25 · openalex publication_date 2008/02/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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 \ensuremathτ_ij as dynamical objects, introduce new parameters, such as the relaxation times describing nonequilibrium behavior of the elements \ensuremathτ_ij. By considering linear response theory and entropy constraints, we show how the additional parameters are related to fluctuations of \ensuremathτ_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.

Citations

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• From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory
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• Experimental and theoretical challenges in the search for the quark–gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions
• Meteorite from the Moon: Petrology of Terrae Clasts and One Mare Clast in ALHA 81005,9

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