2D Mantle Convection: Grid-Based Thermal Plumes

Convection Drivers

Rayleigh number Ra 10⁴

Viscosity ν 1.00

Heat diffusivity κ 1.50

Bottom heat flux 1.00

Display

Plume Injector

Plume radius 8 cells

Live Readouts

Nusselt Nu

1.00

Rising plumes

Grid / FPS

140×70 · —

How it works

This is the 2D companion to the 3D mantle convection simulator, solved independently rather than a flattened render of the 3D scene. It keeps the same real Boussinesq buoyancy-driven convection physics — a temperature field heated from below and cooled from above, advected by a vorticity-streamfunction velocity field — but computes and displays it through a genuinely different pipeline: a CPU finite-difference grid painted directly onto a 2D canvas, with Lagrangian tracer particles and a live flow-arrow (quiver) overlay the 3D shader-based version has no equivalent for, plus an interactive plume injector for seeding new upwellings by hand.

temperature:  ∂T/∂t + J(ψ,T) = κ∇²T
vorticity:    ∂ω/∂t + J(ψ,ω) = ν∇²ω + Ra·κ·∂T/∂x
stream fn:    ∇²ψ = −ω        (Gauss-Seidel Poisson relaxation)
velocity:     u = ∂ψ/∂y,  v = −∂ψ/∂x
tracers:      dx/dt = u(x,y), dy/dt = v(x,y)   (bilinear-sampled, RK2)

Rayleigh number (Ra) — the ratio of buoyancy to viscous/diffusive damping. Below ≈10³ the field just conducts heat; above that, convection cells and rising plumes appear; push it past 10⁵ for chaotic, time-dependent flow.
Click or drag on the canvas — inject a hot plume seed at that spot; the radius slider controls how wide a patch is perturbed.
Tracers are hundreds of massless markers advected by the same velocity field the temperature rides on — they reveal the actual particle paths inside a convection cell, not just the temperature snapshot.
Flow arrows sample the velocity field on a coarse subgrid so you can see circulation direction and strength directly, independent of the colour map.
Nu (Nusselt number) is the ratio of convective to conductive heat transport through the top boundary; Nu = 1 means the field is purely conducting, no convection yet.

In the real Earth this same buoyancy-driven overturning of solid but ductile mantle rock — heated by the core, cooled at the crust — is the engine behind plate tectonics, continental drift and volcanic hotspots such as the plume that built the Hawaiian island chain.

Click or drag — seed a hot plume

T = 0 (cold crust, top) T = heat flux (hot core, bottom)