A subgrid-scale resistivity for magnetohydrodynamics

In this paper an investigation is made of dissipation of small scale magnetic fields embedded in a turbulent gas flow using magnetohydrodynamic (MHD) simulations, under conditions suggested by the outer layers of the Sun, where heat is transported by turbulent convection (as estimated by fluid and magnetic Reynolds numbers), and dissipation is occurring on small scales. The large eddy simulation approach is utilized along with a model for the unresolved scales. Although a significant amount of work on modeling the small scales has been done for hydrodynamic turbulence, the application to MHD has received little attention. This paper specifically deals with the small scale dissipation of magnetic fields and thus a so-called subgrid-scale resistivity is postulated and then tested using a series of two-dimensional numerical simulations. An attempt is made to clarify the advantages and uncertainties of using this new formulation of turbulent resistivity in MHD and suggest areas for improvement and further application.