Parker, starting from a uniform axial magnetic field straddling from one boundary plane to another, subject to continuous independent footpoint motions in either photosphere. This does not imply that we have fully solved the coronal heating problem as due to footpoint dragging by the photospheric velocity field.

A number of relevant effects have been neglected: first, the field line expansion between the photosphere and corona, which, if the photospheric flux is confined to bundles in granular and supergranular network lanes, would allow the mapping of the photospheric velocity field to the coronal volume to contain discontinuities. We are presently carrying out a dedicated set of simulations to capture this effect. Second, the projection of the 3D photospheric velocity to 2D coronal base motions parallel to the photosphere also introduces compressibility in the forcing flow, again neglected here. Third, we have considered stationary photospheric flows. The effect of a finite eddy-turnover time in the flow was considered in [@ein96; @georg98] in 2 dimensions, and in the “3 dimensional” shell model calculations of [@buc07]. These showed that time-dependence does not change things substantially provided the flow pattern does not contain degenerate symmetries, a fact confirmed by shorter simulations we defer to a 