Analysis of the simulation with 50% of perturbations. Top: σ_num (see Eq. (3)) in blue, and the relative difference between σ_num and σ_an (see Eq. (4)) in purple for each output. Bottom: momentum in the disk (in violet) compared to the absolute value of the difference between σ_num and σ_an (in beige). We see that is less than 2.5% and that this difference is smaller than the momentum contained in the disk. The disk thus results in the physics we describe in Sect. 2.2.