🌋 Plate Tectonics Simulator: Lithosphere Cooling, Seafloor Depth and Slab Pull (2D Cross-Section)

Why the ocean floor gets deeper with age

New plate forms at the ridge at the mantle temperature Tm. As it moves away at speed u it cools from the top by conduction. For a half-space the temperature is T(z,t) = Tm erf( z / (2 √(κt)) ), with age t = x/u and thermal diffusivity κ = 10-6 m²/s. The plate "thickness" (the 90 % isotherm) is h = 2.33 √(κt) and grows as the square root of age, about 100 km at 80 Myr.

Isostasy: depth and heat flow

Cooler rock is denser, ρ = ρm(1 + α(Tm - T)), so the column sinks until pressure balances. Integrating the excess density gives the subsidence w(t) = 2 α ρm Tm / (ρm - ρw) · √(κt/π), so depth is d = dridge + w (about 350 m per √Myr). The surface heat flow is q = k Tm / √(π κ t), falling as 1/√t.

Driving forces

Ridge push is the horizontal pressure difference caused by the elevated, hot ridge: Frp = g α ρm Tm κ t (1 + 2 ρm α Tm / (π(ρm - ρw))). Slab pull is the negative buoyancy of the cold slab hanging in the mantle: Fsp = g ρm α Tm · 2√(κt/π) · Ls sinθ, where Ls is the slab length and θ its dip. Older plates pull harder, which is why fast plates (Pacific) are attached to long subduction zones.

Honest simplifications

The model uses a half-space with constant properties (no plate-thickness plateau for ages above about 80 Myr, no radiogenic heating, no hydrothermal heat loss near the ridge), a straight slab with no phase changes, and neglects basal drag, mantle viscosity and slab resistance, so the forces are order-of-magnitude (10¹² to 10¹³ N per metre of trench), not a force balance that predicts the speed. Time on screen is accelerated.

• Raise the spreading rate: the same distance gives a younger, thinner, shallower plate.
• Move the probe from 200 km to 4000 km and watch depth grow like the square root of age.
• Increase the slab length and dip: slab pull overtakes ridge push.
• Compare the analytic and numerical temperature profiles in the third graph.