Local numerical simulations of warped discs

© 2018 The Author(s) We study the hydrodynamical stability of the laminar flows associated with warped astrophysical discs using numerical simulations of warped shearing boxes. We recover linear growth rates reported previously due to a parametric resonance of inertial waves, and show that the non-linear saturated state can significantly reduce the laminar flows, meaning that the warp would evolve on much longer time-scales than would be concluded from the internal torques due to these laminar flows. Towards larger warp amplitudes, we find first of all a reversal of angular momentum flux, indicating that the mass distribution would evolve in an antidiffusive manner, and secondly that the linear growth rates disappear, possibly because of the very strong shear in the laminar flows in this regime. For discs with small enough viscosity, a non-linear state can still be found when linear growth rates are absent by introducing a large enough perturbation, either by starting from a non-linear state obtained at smaller warp amplitude, or by starting from a state with no laminar flows