Abstract
Turbulence in compressible plasma plays a key role in many areas of
astrophysics and engineering. The extreme plasma parameters in these
environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows,
however, make direct numerical simulations computationally intractable even for
the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem
one can use subgrid-scale (SGS) closures -- models for the influence of
unresolved, subgrid-scales on the resolved ones. In this work we propose and
validate a set of constant coefficient closures for the resolved, compressible,
ideal MHD equations. The subgrid-scale energies are modeled 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 and magnetic field gradients. To verify the closures we conduct a
priori tests over 137 simulation snapshots from two different codes with
varying ratios of thermal to magnetic pressure (\$\beta\_p = 0.25, 1,
2.5, 5, 25\$) and sonic Mach numbers (\$M\_s = 2, 2.5, 4\$). Furthermore, we make a
comparison to traditional, phenomenological eddy-viscosity and
\$\alpha-\beta-\gamma\$ closures. We find only mediocre performance of the
kinetic eddy-viscosity and \$\alpha-\beta-\gamma\$ closures, and that the
magnetic eddy-viscosity closure is poorly correlated with the simulation data.
Moreover, three of five coefficients of the traditional closures exhibit a
significant spread in values. In contrast, our new closures demonstrate
consistently high correlation and constant coefficient values over time and and
over the wide range of parameters tested. Important aspects in compressible MHD
turbulence such as the bi-directional energy cascade, turbulent magnetic
pressure and proper alignment of the EMF are well described by our new
closures.
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