Convection in a planetary body Geosciences 519 Natalie D. Murray April 2, 2002

Convection Process of heat transfer ( from hotter to colder regions) by the bulk motion of a fluid More efficient in heat transfer than conduction Needs: Temperature gradient Gravity

Temperature structure of the mantle– superadiabatic temperature gradient due to heating from beneath (from the core) and radiogenic heat production

Buoyancy Parcel – unit volume of a fluid Adiabatic process – no exchange of heat with surroundings Simple process : Parcel is heated from below Temperature increases causing density changes Density of parcel is less than that of surrounding material Parcel is more buoyant and will rise Since the temperature gradient is superadiabatic and the parcel rises adiabatically, the parcel is warmer than the surroundings and will continue to rise.

Navier-Strokes Equations Momentum equation Mass Conservation equation Conservation of Energy Hydrostatic Equation

Boussinesq Approximation Density variations are ignored except when coupled with gravity and give rise to buoyancy (gravitational force) Prandtl Number Virtually infinite in the mantle Inertial forces are insignificant Convection depends on pressure, temperature and viscosity

Forces opposing convection Viscosity – opposes fluid flow (for the Mantle – about the same as for steel 1E20 Pa s) Thermal diffusivity - suppress the temperature fluctuation by causing the rising plume of hot fluid to equilibriate with surrounding fluid (weakens the buoyancy force)

Rayleigh Number Ratio of buoyancy force to the viscous – diffusive force Convection due to superadiabatic temperature gradient Convection due to radiogenic heat Lowrie pg 328 Critical Rayleigh Number – value that if exceeded convection is certain Rayleigh Number for the mantle is super critical Thermal expansion coeff – the more a fluid expands, the more it’s density is lowered Typical values for coefficients can be found on Lowrie pg 328 Table 6.2

Stability

Simple Convective Cell

Rayleigh-Benard Convection Simple model of convection Thermal convection – transfer of heat through a fluid Parcel will rise to the level of neutral buoyancy The hot layer will try to rise while the cold layer will try to sink. Breaks up into convective cells In the form of rolls, hexagon cells, etc.

Rayleigh-Benard Convection

Rayleigh-Benard Convection

Convective Cells in the Mantle

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