Convective Overstability in Accretion Disks: Three-dimensional Linear Analysis and Nonlinear Saturation

Abstract

Recently, Klahr & Hubbard claimed that a hydrodynamical linear overstability exists in protoplanetary disks, powered by buoyancy in the presence of thermal relaxation. We analyze this claim, confirming it through rigorous compressible linear analysis. We model the system numerically, reproducing the linear growth rate for all cases studied. We also study the saturated properties of the overstability in the shearing box, finding that the saturated state produces finite amplitude fluctuations strong enough to trigger the subcritical baroclinic instability (SBI). Saturation leads to a fast burst of enstrophy in the box, and a large-scale vortex develops in the course of the next ≈100 orbits. The amount of angular momentum transport achieved is of the order of α ≈10^(–3), as in compressible SBI models. For the first time, a self-sustained three-dimensional vortex is produced from linear amplitude perturbation of a quiescent base state.