  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 $\alpha_{\rm diff} \sim (0.2-1.2) \times
10^{-2}$. 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.
