Constraining turbulence mixing strength in transitional discs with planets using SPHERE and ALMA

We investigate the effect that the turbulent mixing strength parameter $\alpha_{\rm{turb}}$ plays on near-infrared polarimetric and sub-millimetre interferometric imaging observations of transitional discs (TDs) with a gap carved by a planet. We generate synthetic observations of these objects with ALMA and VLT/SPHERE-ZIMPOL by combining hydrodynamical, dust evolution, radiative transfer and instrument models for values of $\alpha_{\rm{turb}}=[10^{-4}, 10^{-3}, 10^{-2}]$. We find that, through a combination of effects on the viscosity of the gas, the turbulent mixing and dust evolution processes, $\alpha_{\rm{turb}}$ strongly affects the morphology of the dust distribution that can be traced with these observations. We constrain the value of $\alpha_{\rm{turb}}$ to be within an order of magnitude of $10^{-3}$ in TD sources that show cavities in sub-mm continuum images while featuring continuous distribution of dust or smaller cavities in NIR-polarimetric images.