  Theoretical models of the ionization state in protoplanetary disks suggest
the existence of large areas with low ionization and weak coupling between the
gas and magnetic fields. In this regime hydrodynamical instabilities may become
important. In this work we investigate the gas and dust structure and dynamics
for a typical T Tauri system under the influence of the vertical shear
instability (VSI). We use global 3D radiation hydrodynamics simulations
covering all $360^\circ$ of azimuth with embedded particles of 0.1 and 1mm
size, evolved for 400 orbits. Stellar irradiation heating is included with
opacities for 0.1- to 10-$\mu$m-sized dust. Saturated VSI turbulence produces a
stress-to-pressure ratio of $\alpha \simeq 10^{-4}$. The value of $\alpha$ is
lowest within 30~au of the star, where thermal relaxation is slower relative to
the orbital period and approaches the rate below which VSI is cut off. The rise
in $\alpha$ from 20 to 30~au causes a dip in the surface density near 35~au,
leading to Rossby wave instability and the generation of a stationary,
long-lived vortex spanning about 4~au in radius and 40~au in azimuth. Our
results confirm previous findings that mm size grains are strongly vertically
mixed by the VSI. The scale height aspect ratio for 1mm grains is determined to
be 0.037, much higher than the value $H/r=0.007$ obtained from millimeter-wave
observations of the HL~Tau system. The measured aspect ratio is better fit by
non-ideal MHD models. In our VSI turbulence model, the mm grains drift radially
inwards and many are trapped and concentrated inside the vortex. The turbulence
induces a velocity dispersion of $\sim 12$~m/s for the mm grains, indicating
that grain-grain collisions could lead to fragmentation.
