  We investigate the dynamics of r modes at amplitudes in the nonlinear regime
for rapidly but uniformly rotating neutron stars with a polytropic equation of
state. For this, we perform three-dimensional relativistic hydrodynamical
simulations, making the simplifying assumption of a fixed spacetime. We find
that for initial dimensionless amplitudes around three, r modes decay on
timescales around ten oscillation periods, while at amplitudes of order unity,
they are stable over the evolution timescale. Together with the decay, a strong
differential rotation develops, conserving the total angular momentum, with
angular velocities in the range 0.5..1.2 of the initial one. By comparing two
models, we found that increasing rotation slows down the r-mode decay. We
present r-mode eigenfunctions and frequencies, and compare them to known
analytic results for slowly rotating Newtonian stars. As a diagnostic tool, we
discuss conserved energy and angular momentum for the case of a fixed
axisymmetric background metric and introduce a measure for the energy of
non-axisymmetric fluid oscillation modes.
