The breakup of discrete auroral arcs on closed field lines is modeled by nu
merical calculations of nonlinear magnetohydrodynamics in a cavity. The bou
ndary conditions are shown to be crucially important in determining the ava
ilable mechanisms for nonlinear evolution and breakup of the are. Nonlinear
evolution is inhibited if the sign of the electric field is reversed in a
reflecting Alfven wave. The weaker the shear time of the are compared with
the Alfven wave travel time across the cavity, the more strongly the nonlin
ear evolution is inhibited. Because different transverse length scales have
different reflection properties related to their ability to pass through t
he auroral acceleration region, arcs with small horizontal scales are subje
ct to the Kelvin-Helmholtz shear flow instability while large horizontal sc
ales are not. Parallels are drawn to the observed breakup phenomenology of
small-scale and large-scale area.