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