  A simplified non-linear numerical model for the development of incompressible
magnetohydrodynamics (MHD) in the presence of a strong magnetic field B0 and
stratification, nicknamed Shell-Atm, is presented. In planes orthogonal to the
mean field, the non-linear incompressible dynamics is replaced by 2D
shell-models for the complex variables u and b, allowing one to reach large
Reynolds numbers while at the same time carrying out sufficiently long time
integrations to obtain a good statistics at moderate computational cost. The
shell-models of different planes are coupled by Alfven waves propagating along
B0. The model may be applied to open or closed magnetic field configurations
where the axial field dominates and the plasma pressure is low; here we apply
it to the specific case of a magnetic loop of the solar corona heated via
turbulence driven by photospheric motions, and we use statistics for its
analysis. The Alfven waves interact non-linearly and form turbulent spectra in
the directions perpendicular and, via propagation, also parallel to the mean
field. A heating function is obtained, and is shown to be intermittent; the
average heating is consistent with values required for sustaining a hot corona,
and is proportional to the aspect ratio of the loop to the power -1.5;
characteristic properties of heating events are distributed as power-laws.
Cross-correlations show a delay of dissipation compared to energy content.
