The 3D version renders a perspective cutaway of the ice sheet with a tube whose radius you watch grow. This 2D companion solves the identical Röthlisberger/Nye ODE system — independently re-implemented here, not shared code — but never draws a camera view of the ice at all. Instead it plots the same two state variables (channel area S, lake volume V) as two 2D-native charts:
Effective pressure: N = ρ_i g H_ice − ρ_w g h_lake
Melt-opening: dS/dt|open = Q·(dΦ/dx) / (ρ_i L) ~ S^(4/3)
Creep closure: dS/dt|close = 2 A S (N / n)^n, n = 3 ~ S^1
Discharge: Q ≈ k · S^(4/3)
Left chart — live hydrograph: discharge Q scrolls left-to-right against elapsed time, exactly the instrument trace a glaciologist would read off a stream gauge downstream of a real jökulhlaup.
Right chart — phase plane: because Sopen scales as S^(4/3) but Sclose only as S^1, the point where they balance is an unstable threshold, not a stable rest state — below it the trajectory collapses toward the residual creep-closed channel; above it, opening outruns closure and the point runs away toward high S / collapsing N. Watching the (N, S) dot trace that runaway loop makes the instability visible as geometry, which a rendered tube cannot show directly.
The small schematic strip along the top is a genuine 2D cross-section sketch (bed / ice / lake / channel), not a flattened 3D render — it exists only to anchor what N, S and Q physically correspond to.
- Ice thickness sets ρ_i g H_ice — thicker ice raises the flotation threshold and resists opening more.
- Channel slope sets dΦ/dx, the potential gradient driving viscous-dissipation melting.
- Meltwater recharge is the steady inflow refilling the lake between outbursts.
- Trigger Outburst seeds S ≈ 0.05 m² — enough, if above the unstable threshold for the current settings, to run away on its own.