We present numerical studies of the nonlinear, resistive magnetohydrodynami
c (MHD) evolution of coronal loops. For these simulations we assume that th
e loops carry no net current, as might be expected if the loop had evolved
because of vortex flows. Furthermore, the initial equilibrium is taken to b
e a cylindrical flux tube with line-tied ends. For a given amount of twist
in the magnetic field, it is well known that once such a loop exceeds a cri
tical length it becomes unstable to ideal MHD instabilities. The early evol
ution of these instabilities generates large current concentrations. First
we show that these current concentrations are consistent with the formation
of a current sheet. Magnetic reconnection can only occur in the vicinity o
f these current concentrations, and we therefore couple the resistivity to
the local current density. This has the advantage of avoiding resistive dif
fusion in regions where it should be negligible. We demonstrate the importa
nce of this procedure by comparison with simulations based on a uniform res
istivity. From-our numerical experiments we are able to estimate some obser
vational signatures for unstable coronal loops. These signatures include th
e timescale of the loop brightening, the temperature increase, and the ener
gy released and the predicted observable how speeds. Finally, we discuss to
what extent these observational signatures are consistent with the propert
ies of transient brightening loops.