  Nonlinear evolution of the gravitational radiation (GR) driven instability in
the r-modes of neutron stars is studied by full numerical 3D hydrodynamical
simulations. The growth of the r-mode instability is found to be limited by the
formation of shocks and breaking waves when the dimensionless amplitude of the
mode grows to about three in value. This maximum mode amplitude is shown by
numerical tests to be rather insensitive to the strength of the GR driving
force. Upper limits on the strengths of possible nonlinear mode--mode coupling
are inferred. Previously unpublished details of the numerical techniques used
are presented, and the results of numerous calibration runs are discussed.
