  Rossby waves (r-modes) in rapidly rotating neutron stars are unstable because
of the emission of gravitational radiation. We study saturation of this
instability by nonlinear transfer of energy to stellar "inertial" oscillation
modes. We present detailed calculations of stellar inertial modes in the WKB
limit, their linear damping by bulk and shear viscosity, and the nonlinear
coupling forces among these modes. The saturation amplitude is derived in the
extreme limits of strong or weak driving by radiation reaction, as compared to
the damping rate of low order inertial modes. We find the saturation energy is
{\it extremely small}, at least four orders of magnitude smaller than that
found by previous investigators. We discuss the consequences of this result for
spin evolution of young neutron stars, and neutron stars being spun up by
accretion in Low Mass X-ray Binaries.We also discuss the detection of these
gravitational waves by LIGO.
