Resolving high Reynolds numbers in SPH simulations of subsonic turbulence

Accounting for the Reynolds number is critical in numerical simulations of turbulence, particularly for subsonic flow. For Smoothed Particle Hydrodynamics (SPH) with constant artificial viscosity coefficient α, it is shown that the effective Reynolds number in the absence of explicit physical viscosity terms scales linearly with the Mach number — compared to mesh schemes, where the effective Reynolds number is largely independent of the flow velocity. As a result, SPH simulations with α = 1 will have low Reynolds numbers in the subsonic regime compared to mesh codes, which may be insufficient to resolve turbulent flow. This explains the failure of Bauer & Springel (2011, arXiv:1109.4413v1) to find agreement between the moving-mesh code AREPO and the GADGET SPH code on simulations of driven, subsonic (v ∼ 0.3cs) turbulence appropriate to the intergalactic/intracluster medium, where it was alleged that SPH is somehow fundamentally incapable of producing a Kolmogorov-like turbulent cascade. We show that turbulent flow with a Kolmogorov spectrum can be easily recovered by employing standard methods for reducing α away from shocks.