Self-Destructing Spiral Waves: Global Simulations of a Spiral Wave Instability in Accretion Disks

Abstract

We present results from a suite of three-dimensional global hydrodynamic simulations which show that spiral density waves propagating in circumstellar disks are unstable to the growth of a parametric instability that leads to break-down of the flow into turbulence. This spiral wave instability (SWI) arises from a resonant interaction between pairs of inertial waves, or inertial-gravity waves, and the background spiral wave. The development of the instability in the linear regime involves the growth of a broad spectrum of inertial modes, with growth rates on the order of the orbital time, and results in a nonlinear saturated state in which turbulent velocity perturbations are of a similar magnitude to those induced by the spiral wave. The turbulence induces angular momentum transport, and vertical mixing, at a rate that depends locally on the amplitude of the spiral wave (we obtain a stress parameter $\alpha \sim 5 \times 10^{-4}$ in our reference model). The instability is found to operate in a wide-range of disk models, including those with isothermal or adiabatic equations of state, and in viscous disks where the dimensionless kinematic viscosity $\nu\le 10^{-5}$. This robustness suggests that the instability will have applications to a broad range of astrophysical disk-related phenomena, including those in close binary systems, planets embedded in protoplanetary disks (including Jupiter in our own Solar System) and FU Orionis outburst models. Further work is required to determine the nature of the instability, and to evaluate its observational consequences, in physically more complete disk models than we have considered in this paper.