Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence

Turbulence in compressible plasma plays a key role inmany areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. highReynolds numbers, supersonic and super-Alfvenic flows, however,make direct numerical simulations computationally intractable even for the simplest treatment—magnetohydrodynamics (MHD). To overcome this problemone can use subgrid-scale (SGS) closures—models for the influence of unresolved, subgrid-scales on the resolved ones. In this workwe propose and validate a set of constant coefficient closures for the resolved, compressible, idealMHDequations. The SGS energies aremodeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity andmagnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from twodifferent codes with varying ratios of thermal tomagnetic pressure (β = 0.25, 1, 2.5, 5, 25 p ) and sonicMach numbers ( = M 2, 2.5, 4 s ). Furthermore, wemake a comparison to traditional, phenomenological eddy-viscosity andα β γ − − closures.We find onlymediocre performance of the kinetic eddy-viscosity andα β γ − − closures, and that themagnetic eddy-viscosity closure is poorly correlatedwith the simulation data.Moreover, three offive coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlations and constant coefficient values over time and over thewide range of parameters tested. Important aspects in compressibleMHD turbulence such as the bi-directional energy cascade, turbulentmagnetic pressure and proper alignment of the EMF arewell described by our new closures.