Finite Reynolds number effect on substantial inertial range in incompressible magnetohydrodynamic turbulence

We investigate how finite Reynolds number affects the width of the Inertial Range (IR) in magnetohydrodynamic (MHD) turbulence. A set of high-resolution incompressible MHD simulation data is employed, with Taylor Reynolds Number $R\phantom{\rule{0}{0ex}}{e}_{\ensuremath{\lambda}}$ ranging from about 200 to 400. The IR width is quantified using third-order laws. A semi-empirical model for second-order structure functions is established and applied to the MHD von Karman-Howarth equation, determining IR boundaries for given Reynolds numbers. This model allows extrapolation of $R\phantom{\rule{0}{0ex}}{e}_{\ensuremath{\lambda}}$ beyond the reach of current simulations or experiments. We suggest that establishing a two-decade IR in MHD turbulence requires $R\phantom{\rule{0}{0ex}}{e}_{\ensuremath{\lambda}}$ to be at least 1,500.