Mantle Convection Simulator: Rayleigh-Bénard Flow in Earth's Interior

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Nu ≈ 7.8 — mantle transports ~8× more heat than pure conduction

At Ra = 10,000, mantle convection enhances heat transport by a factor of ~7.8 compared to conduction alone. Convection velocity is ~2 cm/yr and the overturn time is ~150 Myr.

Formula

Ra = αgΔTD³/(κν) (Rayleigh number)
Nu ≈ 0.195 × Ra^(0.3) (Nusselt number scaling)
v ≈ κ/D × Ra^(2/3) (convection velocity)

The Engine Beneath Our Feet

Earth's mantle — the 2,900-km-thick layer between crust and core — convects like a pot of extremely viscous syrup heated from below. Despite viscosities a billion billion times that of water, mantle rock flows at centimeters per year over millions of years. This convection is the fundamental engine of plate tectonics: it drives plate motion, creates mid-ocean ridges, powers subduction, and generates the magnetic field through core convection.

Rayleigh-Bénard Instability

When a fluid layer is heated from below, convection begins once the Rayleigh number exceeds a critical value (~1100). Earth's mantle Ra ≈ 10⁷, so convection is vigorous and time-dependent. Hot material rises in plumes and sheets; cold material sinks as slabs. The boundary layers — hot at the base, cold at the top — are where temperature changes most rapidly, analogous to the lithosphere (cold) and D'' layer (hot).

Convection Patterns

Mantle convection exhibits complex, three-dimensional, time-dependent patterns. Upwelling plumes (hotspots like Hawaii) are narrow and cylindrical; downwelling slabs (subduction zones) are planar sheets. Large-scale flow organizes into cells spanning thousands of kilometers. At high Rayleigh numbers, the flow becomes increasingly chaotic with smaller-scale instabilities, time-varying planforms, and complex interactions between plumes and plates.

Heat Budget and Cooling

Earth loses about 44 terawatts of heat through its surface — roughly half from radioactive decay in the mantle and crust, and half from primordial heat of formation. Convection transports this heat far more efficiently than conduction alone, characterized by the Nusselt number Nu ~ Ra^(0.3). Without mantle convection, Earth's surface heat flux would be ~8× lower, the interior far hotter, and plate tectonics as we know it would not exist.

FAQ

What drives mantle convection?

Mantle convection is driven by the temperature difference between Earth's hot core (~4000°C at the core-mantle boundary) and its cool surface (~0–20°C). This thermal gradient, combined with mantle rock that behaves as an extremely viscous fluid over geological timescales, creates convective circulation described by the Rayleigh number.

What is the Rayleigh number?

The Rayleigh number Ra = αgΔTD³/(κη/ρ) determines whether convection occurs and how vigorous it is. Earth's mantle has Ra ≈ 10⁷, far above the critical value of ~1100, ensuring vigorous, time-dependent convection. Higher Ra means faster flow, thinner boundary layers, and more chaotic dynamics.

Is mantle convection whole-mantle or layered?

Seismic tomography reveals both patterns. Some subducted slabs penetrate to the core-mantle boundary (whole-mantle flow), while others accumulate near the 660 km transition zone (partial layering). The current consensus is intermittent whole-mantle convection with complications from phase transitions and viscosity contrasts.

How fast does the mantle flow?

Mantle convection velocities are typically 1–10 cm/yr — about as fast as fingernails grow. Despite these glacial speeds, over geological time they move continents thousands of kilometers, recycle the entire ocean floor every ~200 million years, and transport ~44 TW of heat from Earth's interior to the surface.

Sources

Embed

<iframe src="https://homo-deus.com/lab/plate-tectonics/mantle-convection/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub