This 2D version replaces the 3D scene with two computed panels: a thermal boundary-layer field gridded across downdip distance and depth-into-slab, and a cross-section diagram driven entirely by that field.
Half-space cooling (per column, exact heat-eq. solution):
T(z,x)/T_m = erf( z / (2·√(κ·age(x))) ) age(x) = age_trench + x / v_conv
90%-of-mantle isotherm defines the boundary-layer thickness:
h(x) = 2·erf⁻¹(0.9)·√(κ·age(x)) ≈ 2.32·√(κ·age(x))
Slab pull is the field integrated along the slab, not a single point:
F_SP = ∫₀^L Δρ·g·h(x) dx (numerically, over the grid)
Rollback / back-arc rate follow as before:
v_roll = F_SP / (η·k_drag) v_BA = v_roll − v_overriding
- Each grid column is an independent 1D half-space-cooling solution — the exact solution of the 1D heat equation for a surface suddenly held at a fixed temperature. A column farther from the trench has been in the mantle longer (age(x) grows with x/v_conv), so it has thickened and cooled further — you can watch the boundary layer visibly thicken left-to-right as convergence rate drops.
- The bright isotherm line traces h(x): the same 90%-isotherm criterion that gives the 3D version's 2.32 constant, verified here by direct numerical inversion of the erf field rather than assumed.
- Slab pull is now a true integral of the local buoyancy over the whole subducted length, instead of one thickness value multiplied by a capped length — a distinct but physically consistent way to reach the same force-balance conclusion.
- The cross-section below places the volcanic arc where the slab's dip angle carries it past ~110 km depth, and draws the back-arc basin (or compressional overlap) to scale from the live v_BA integration.