  We present three-dimensional numerical simulations of the rise and
fragmentation of twisted, initially horizontal magnetic flux tubes which evolve
into emerging Omega-loops. The flux tubes rise buoyantly through an
adiabatically stratified plasma that represents the solar convection zone. The
MHD equations are solved in the anelastic approximation, and the results are
compared with studies of flux tube fragmentation in two dimensions. We find
that if the initial amount of field line twist is below a critical value, the
degree of fragmentation at the apex of a rising Omega-loop depends on its
three-dimensional geometry: the greater the apex curvature of a given
Omega-loop, the lesser the degree of fragmentation of the loop as it approaches
the photosphere. Thus, the amount of initial twist necessary for the loop to
retain its cohesion can be reduced substantially from the two-dimensional
limit. The simulations also suggest that as a fragmented flux tube emerges
through a relatively quiet portion of the solar disk, extended crescent-shaped
magnetic features of opposite polarity should form and steadily recede from one
another. These features eventually coalesce after the fragmented portion of the
Omega-loop emerges through the photosphere.
