  We model the nonlinear saturation of the r-mode instability via three-mode
couplings and the effects of the instability on the spin evolution of young
neutron stars. We include one mode triplet consisting of the r-mode and two
near resonant inertial modes that couple to it. We find that the spectrum of
evolutions is more diverse than previously thought. The evolution of the star
is dynamic and initially dominated by fast neutrino cooling. Nonlinear effects
become important when the r-mode amplitude grows above its first parametric
instability threshold. The balance between neutrino cooling and viscous heating
plays an important role in the evolution. Depending on the initial r-mode
amplitude, and on the strength of the viscosity and of the cooling this balance
can occur at different temperatures. If thermal equilibrium occurs on the
r-mode stability curve, where gravitational driving equals viscous damping, the
evolution may be adequately described by a one-mode model. Otherwise, nonlinear
effects are important and lead to various more complicated scenarios. Once
thermal balance occurs, the star spins-down oscillating between thermal
equilibrium states until the instability is no longer active. For lower
viscosity we observe runaway behavior in which the r-mode amplitude passes
several parametric instability thresholds. In this case more modes need to be
included to model the evolution accurately. In the most optimistic case, we
find that gravitational radiation from the r-mode instability in a very young,
fast spinning neutron star within about 1 Mpc of Earth may be detectable by
advanced LIGO for years, and perhaps decades, after formation. Details
regarding the amplitude and duration of the emission depend on the internal
dissipation of the modes of the star, which would be probed by such detections.
