  Measurements of average velocity profiles in a bubble raft subjected to slow,
steady-shear demonstrate the coexistence between a flowing state and a jammed
state similar to that observed for three-dimensional foams and emulsions
[Coussot {\it et al,}, Phys. Rev. Lett. {\bf 88}, 218301 (2002)]. For
sufficiently slow shear, the flow is generated by nonlinear topological
rearrangements. We report on the connection between this short-time motion of
the bubbles and the long-time averages. We find that velocity profiles for
individual rearrangement events fluctuate, but a smooth, average velocity is
reached after averaging over only a relatively few events.
