Effect of extra vertical force on the self-gravity wakes. In a) three examples of simulation with self-consistent vertical forces (left), and with hybrid method, using Ω_z/Ω = 4.5 and 7.5 (middle and right frames). A fixed r_h = 0.70 is assumed. In b) similar examples for strong wakes, but with varying r_h so that they yield roughly the same ν_tot ≈ 100–160 ⋅ 10⁻⁴m²/s, when internal densities ρ = 250 kg m⁻³, 450 kg m⁻³ and 750 kg m⁻³ are assumed, respectively. Note that since Σ = 350 kg m⁻² is fixed, the particle size R ∝ 1/ρ. The upper frames show face-on snapshots of the system, limited to 4λ_cr × 4λ_cr regions. In the edge-on snapshots, the vertical scale is exaggerated by a factor of 5. The insert images in b) show cuts in xz plane through the positions indicated by the short vertical bars in the upper frames. The blue rectangles and ellipses indicate the size and shape of the fitted slab models, using Eqs. (23) and (24), assuming wake separation λ = λ_cr; the labels indicate the wake’s height/width ratio for Eq. (23). The vertical projections in the lower frames are calculated by sampling only particles around the grey y = 0 line marked in the upper snapshots.