  We study the dynamical evolution of a large amplitude r-mode by numerical
simulations. R-modes in neutron stars are unstable growing modes, driven by
gravitational radiation reaction. In these simulations, r-modes of amplitude
unity or above are destroyed by a catastrophic decay: A large amplitude r-mode
gradually leaks energy into other fluid modes, which in turn act nonlinearly
with the r-mode, leading to the onset of the rapid decay. As a result the
r-mode suddenly breaks down into a differentially rotating configuration. The
catastrophic decay does not appear to be related to shock waves at the star's
surface. The limit it imposes on the r-mode amplitude is significantly smaller
than that suggested by previous fully nonlinear numerical simulations.
