The Spiral Wave Instability Induced by a Giant Planet: I. Particle Stirring in the Inner Regions of Protoplanetary Disks

We have recently shown that spiral density waves propagating in accretion disks can undergo a parametric instability by resonantly coupling with and transferring energy into pairs of inertial waves (or inertial-gravity waves when buoyancy is important). In this paper, we perform inviscid three-dimensional global hydrodynamic simulations to examine the growth and consequence of this instability operating on the spiral waves driven by a Jupiter-mass planet in a protoplanetary disk. We find that the spiral waves are destabilized via the spiral wave instability (SWI), generating hydrodynamic turbulence and sustained radially-alternating vertical flows that appear to be associated with long wavelength inertial modes. In the interval $0.3~R_p \leq R \leq 0.7~R_p$, where $R_p$ denotes the semi-major axis of the planetary orbit (assumed to be 5~au), the estimated vertical diffusion rate associated with the turbulence is characterized by $α_{\rm diff} \sim (0.2-1.2) \times 10^{-2}$. For the disk model considered here, the diffusion rate is such that particles with sizes up to several centimeters are vertically mixed within the first pressure scale height. This suggests that the instability of spiral waves launched by a giant planet can significantly disperse solid particles and trace chemical species from the midplane. In planet formation models where the continuous local production of chondrules/pebbles occurs over Myr time scales to provide a feedstock for pebble accretion onto these bodies, this stirring of solid particles may add a time constraint: planetary embryos and large asteroids have to form before a gas giant forms in the outer disk, otherwise the SWI will significantly decrease the chondrule/pebble accretion efficiency.