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We study the dynamical evolution of a large amplitude r-mode by numericalsimulations. R-modes in neutron stars are unstable growing modes, driven bygravitational radiation reaction. In these simulations, r-modes of amplitudeunity or above are destroyed by a catastrophic decay: A large amplitude r-modegradually leaks energy into other fluid modes, which in turn act nonlinearlywith the r-mode, leading to the onset of the rapid decay. As a result ther-mode suddenly breaks down into a differentially rotating configuration. Thecatastrophic decay does not appear to be related to shock waves at the star'ssurface. The limit it imposes on the r-mode amplitude is significantly smallerthan that suggested by previous fully nonlinear numerical simulations.Comment: Published in Phys. Rev. D Rapid Comm. 66, 041303(R) (2002

Nonlinearr-modes in neutron stars: Instability of an unstable mode