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The transport of waves and turbulence beyond the photosphere is central tothe coronal heating problem. Turbulence in the quiet solar corona has beenmodeled on the basis of the nearly incompressible magnetohydrodynamic (NI MHD)theory to describe the transport of low-frequency turbulence in open magneticfield regions. It describes the evolution of the coupled majority quasi-2D andminority slab component, driven by the magnetic carpet and advected by asubsonic, sub-Alfvenic flow from the lower corona. In this paper, we couple theNI MHD turbulence transport model with an MHD model of the solar corona tostudy the heating problem in a coronal loop. In a realistic benchmark coronalloop problem, we find that a loop can be heated to ~1.5 million K by transportand dissipation of MHD turbulence described by the NI MHD model. We also findthat the majority 2D component is as important as the minority slab componentin the heating of the coronal loop. We compare our coupled MHD/NI MHD modelresults with a reduced MHD (RMHD) model. An important distinction between thesemodels is that RMHD solves for small-scale velocity and magnetic fieldfluctuations and obtains the actual viscous/resistive dissipation associatedwith their evolution whereas NI MHD evolves scalar moments of the fluctuatingvelocity and magnetic fields and approximates dissipation using an MHDturbulence phenomenology. Despite the basic differences between the models,their simulation results match remarkably well, yielding almost identicalheating rates inside the corona.

Coronal Loop Heating by Nearly Incompressible Magnetohydrodynamic and Reduced Magnetohydrodynamic Turbulence Models