The Interplay of Parametric and Magnetorotational Instabilities in Oscillatory Shear Flows

Abstract

The evolution of warped disks is governed by internal, oscillatory shear flows driven by their distorted geometry. However, these flows are known to be vigorously unstable to a hydrodynamic parametric instability. In many warped systems, this might coexist and compete with the magnetorotational instability (MRI). The interplay of these phenomena and their combined impact on the internal flows has not been studied. To this end, we perform three-dimensional, magnetohydrodynamic unstratified shearing box simulations with an oscillatory radial forcing function to mimic the effects of a warped disk. In the hydrodynamic study, we find that the parametric instability manifests as strong, vertical `elevator' flows that resist the sloshing motion. Above a critical forcing amplitude, these also emerge in our magnetized runs and dominate the vertical stress, although they are partially weakened by the MRI, and hence the system equilibrates with larger radial sloshing flows. Below this critical forcing, the MRI effectively quenches the parametric instability. In all cases, we find that the internal stresses are anisotropic in character and better described by a viscoelastic relationship with the shearing flows. Unfortunately, these important effects are typically unresolved in global simulations of warped disks and are simplified in analytically tractable models. The incorporation of such complex, warp-amplitude-dependent, viscoelastic stresses will sensitively regulate the laminar flow response and inevitably modify the detailed spatio-temporal evolution of warped systems.