  An analytical and numerical treatment is given of a constrained version of
the tectonics model developed by Priest, Heyvaerts, & Title [2002]. We begin
with an initial uniform magnetic field ${\bf B} = B_0 \hat{\bf z}$ that is
line-tied at the surfaces $z = 0$ and $z = L$. This initial configuration is
twisted by photospheric footpoint motion that is assumed to depend on only one
coordinate ($x$) transverse to the initial magnetic field. The geometric
constraints imposed by our assumption precludes the occurrence of reconnection
and secondary instabilities, but enables us to follow for long times the
dissipation of energy due to the effects of resistivity and viscosity. In this
limit, we demonstrate that when the coherence time of random photospheric
footpoint motion is much smaller by several orders of magnitude compared with
the resistive diffusion time, the heating due to Ohmic and viscous dissipation
becomes independent of the resistivity of the plasma. Furthermore, we obtain
scaling relations that suggest that even if reconnection and/or secondary
instabilities were to limit the build-up of magnetic energy in such a model,
the overall heating rate will still be independent of the resistivity.
