Nonlinear effect of R-mode instability in uniformly rotating stars

We investigate the r-mode instability of uniformly rotating stars by means of three dimensional hydrodynamical simulations in Newtonian gravity with radiation reaction We have succeeded in constructing a nonlinear anelastic approximation in the rotating reference frame, which kills the propagation of sound speed, in order to evolve the system beyond the dynamical timescale. When the current multipole contribution is dominant to the r-mode instability (density fluctuation effect is negligible), the instability seems to last for at least hundreds of rotation periods Studies of no anelastic approximation with small amplitude of velocity perturbation may help us for a better understanding.