  Recent work has shown that differential rotation, producing large scale
drifts of fluid elements along stellar latitudes, is an unavoidable feature of
r-modes in the nonlinear theory. We investigate the role of this differential
rotation in the evolution of the l=2 r-mode instability of a newly born, hot,
rapidly rotating neutron star. It is shown that the amplitude of the r-mode
saturates a few hundred seconds after the mode instability sets in. The
saturation amplitude depends on the amount of differential rotation at the time
the instability becomes active and can take values much smaller than unity. It
is also shown that, independently of the saturation amplitude of the mode, the
star spins down to rotation rates that are comparable to the inferred initial
rotation rates of the fastest pulsars associated with supernova remnants.
Finally, it is shown that, when the drift of fluid elements at the time the
instability sets in is significant, most of the initial angular momentum of the
star is transferred to the r-mode and, consequently, almost none is carried
away by gravitational radiation.
