Results of the different substeps as discussed in Sect. 3.4. Top panel: perturbation in radial velocity as determined by FARGO-3D and determined using Eq. (9) with the azimuthal velocity perturbation as a reference. Central panel: perturbation in surface density as determined by FARGO-3D and determined from the perturbation in velocity using Eqs. (14) and (13). Bottom panel: result of the numerical integration to derive the azimuthal velocity perturbation of the dust from the azimuthal velocity of the gas, together with the FARGO-3D results and the azimuthal velocity perturbation as comparison.