# Local numerical simulations of warped discs

## TL;DR

This study uses numerical simulations to analyze the stability and nonlinear behavior of warped astrophysical discs, revealing how warp amplitudes and viscosity influence angular momentum flux and disc evolution timescales.

## Contribution

It provides new insights into the nonlinear saturated states of warped discs and how they affect warp evolution, especially at large amplitudes and low viscosities.

## Key findings

- Linear growth rates are due to parametric resonance of inertial waves.
- Nonlinear saturated states can reduce laminar flows, affecting warp evolution.
- Reversal of angular momentum flux indicates anti-diffusive mass distribution.

## Abstract

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 nonlinear 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 anti-diffusive manner, and second 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 nonlinear state can still be found when linear growth rates are absent by introducing a large enough perturbation, either by starting from a nonlinear state obtained at smaller warp amplitude, or by starting from a state with no laminar flows.