Lava flow - 2D map lab

Thin-film lava flow

For a slow, viscous, gravity-driven sheet (lubrication approximation) the depth-integrated flux is q = ρ g h³ (−∂(z+h)/∂n) / (3μ), where z is the ground height and h the lava thickness. Mass conservation ∂h/∂t + ∇·q = source is solved on a 96 x 96 grid. On a uniform plane of slope α a steady sheet fed with q per unit width has the Nusselt thickness h = (3μq / (ρ g tanα))1/3 and mean speed u = ρ g h² tanα / (3μ).

Viscosity depends strongly on temperature, μ(T) = μ0 exp(−b (T − Tvent)) with b = 0.018 per kelvin, so a few hundred degrees of cooling stiffen the lava by orders of magnitude (graph 3). Heat is advected with the flow and lost at a rate proportional to 1/h (thin lava cools faster); below 760 C the lava is treated as solid crust and stops, which builds levees at the edges and makes thick flows follow valleys.

Honest simplifications

Newtonian rheology (no yield strength), depth-uniform temperature, a single crust threshold instead of a growing crust, no heat release from crystallisation, and the small-slope lubrication approximation. Numbers are representative of basaltic flows, not fitted to a particular eruption. The 3D page is a visual terrain scene; this page uses these physical equations.

• Compare the fluid basalt preset with the viscous one: the thin fast flow runs far, the viscous one piles up near the vent.
• Valley channel: the flow is confined and stays hot in the middle while edges form crust.
• Click on the map to move the vent, or raise cooling strength and watch the flow stall.