Nonlinear evolution of the r-modes in neutron stars

The evolution of a neutron-star r-mode driven unstable by gravitational rad iation is studied here using numerical solutions of the full nonlinear flui d equations. The dimensionless amplitude of the mode grows to order unity b efore strong shocks develop which quickly damp the mode. In this simulation the star loses about 40% of its initial angular momentum and 50% of its ro tational kinetic energy before the mode is damped. The nonlinear evolution causes the fluid to develop strong differential rotation which is concentra ted near the surface and poles of the star.