Suite of MHD simulations. From left to right, the transition width is h₁ = 0.1, 0.2, 0.4 and 0.8. The resulting resistivity profiles are shown in the upper panels. The dashed vertical lines correspond to 2H around the jump center at r = 2.5. The model with h₁ = 0.8 corresponds to a smooth jump from r ≈ 1 to r ≈ 4, i.e., over ≈15 scale heights. Although at different times, all models develop a sharp density bump that goes unstable to the RWI, producing a Rossby vortex (middle panels). The panels, from left to right, correspond to density snapshots at 100, 100, 122, and 232T₀, where T₀ is the orbital period at r = 1. The dashed vertical lines correspond to 2H around the density maximum. The reason for RWI excitation in these cases is because even though the resistivity jump is smooth, the transition in Maxwell stress remains sharp (lower panels). The transition in Reynolds stress is somewhat smoother, but turbulent stresses do not blur gradients in the same way Laplacian viscosity does, and the density bump remains RWI-unstable.