Inverse Reynolds-dominance approach to transient fluid dynamics

May 17, 2022, 4:10 PM


David Wagner (Universita di Firenze)


We consider the evolution equations for the bulk viscous pressure, diffusion current and shear
tensor derived within the second order relativistic dissipative hydrodynamics from kinetic theory.
By matching the higher order moments directly to the dissipative quantities, all terms which are
of second order in the Knudsen number Kn vanish, leaving only terms of order O(Re−1 Kn) and
O(Re−2) in the relaxation equations, where Re−1 is the inverse Reynolds number. We therefore
refer to this scheme as the Inverse Reynolds Dominance (IReD) approach. The remaining (non-
vanishing) transport coefficients can be obtained exclusively in terms of the inverse of the collision
matrix. This procedure fixes unambiguously the relaxation times of the dissipative quantities, which
are no longer related to the eigenvalues of the inverse of the collision matrix. In particular, we find
that the relaxation times corresponding to higher order moments grow as the order of moments
increases, thereby contradicting the separation of scales paradigm. The formal (up to second order)
equivalence with the standard DNMR approach is proven and the connection between the IReD
transport coefficients and the usual DNMR ones is established.

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