  We study numerically the nonlinear dynamics of a shear banding interface in
two dimensional planar shear flow, within the non-local Johnson Segalman model.
Consistent with a recent linear stability analysis, we find that an initially
flat interface is unstable with respect to small undulations for sufficiently
small ratio of the interfacial width $\ell$ to cell length $L_x$. The
instability saturates in finite amplitude interfacial fluctuations. For
decreasing $\ell/L_x$ these undergo a non equilibrium transition from simple
travelling interfacial waves with constant average wall stress, to periodically
rippling waves with a periodic stress response. When multiple shear bands are
present we find erratic interfacial dynamics and a stress response suggesting
low dimensional chaos.
