Illustration of the origin of the increased vertical Reynolds stress in 2D simulations with small Z and τ₀ = 10⁻³ compared to the dust-free simulation as seen in Fig. 6. In the left panels, corresponding to Z = 0.01, the VSI strongly corrugates the dust-layer which results in non-vanishing radial and vertical gradients of f_d which result in a violation of Eq. (40), which is indicated by black colors in the plots labeled ⟨SH₂ ⟩. The largest contribution to the violation is by radial gradients. The right panels correspond to Z = 0.05 where the VSI is too much weakened to cause significant corrugation.