Three-dimensional dust stirring by a giant planet embedded in a protoplanetary disc

The motion of solid particles embedded in gaseous protoplanetary discs is influenced by turbulent fluctuations. Consequently, the dynamics of moderately to weakly coupled solids can be distinctly different from the dynamics of the gas. Additionally, gravitational perturbations from an embedded planet can further impact the dynamics of solids. In this work, we investigate the combined effects of turbulent fluctuations and planetary dust stirring in a protoplanetary disc on three-dimensional dust morphology and on synthetic ALMA continuum observations. We carry out 3D radiative two-fluid (gas + 1-mm-dust) hydrodynamic simulations in which we explicitly model the gravitational perturbation of a Jupiter-mass planet. We derived a new momentum-conserving turbulent diffusion model that introduces a turbulent pressure to the pressureless dust fluid to capture the turbulent transport of dust. The model implicitly captures the effects of orbital oscillations and reproduces the theoretically predicted vertical settling-diffusion equilibrium. We find a Jupiter-mass planet to produce distinct and large-scale three-dimensional flow structures in the mm-sized dust, which vary strongly in space. We quantify these effects by locally measuring an effective vertical diffusivity (equivalent alpha) and find azimuthally averaged values in a range delta(eff) similar to 5 x 10(-3)-2 x 10(-2) and local peaks at values of up to delta(eff) similar to 3 x 10(-1). In synthetic ALMA continuum observations of inclined discs, we find effects of turbulent diffusion to be observable, especially at disc edges, and effects of planetary dust stirring in edge-on observations.