Convection with internal heat sources and thermal turbulence in the Earth's mantle

Abstract

SUMMARY The influence of internal heat sources on mantle convection is investigated using numerical calculations of 2-D thermal convection in an infinite Prandtl number, incompressible fluid. The geometry is a cylindrical annulus with inner and outer radii in proportion to the whole mantle. Time-dependent calculations are made starting from random initial conditions, with Rayleigh numbers RaT (based on boundary-temperature difference) and Ra, (based on internal-heat production) in the range 1dsRaTs lo7 and OsRa,524RaT. At fixed RaT, increasing Ra, results in transitions in flow structure from steady cells, to a pattern of stationary cells with time-variable amplitude, and finally to thermally turbulent convection with a non-stationary cell count. For RaT 10' and Ra, >RaT approximately, the travelling plumes disrupt the large-scale circulation, producing turbulent convection. At Ra, = lo7 the flow is fully developed thermal turbulence, and for Ra, > 0, consists of a rapidly fluctuating, irregular flow driven by transient rising and sinking sheets of buoyant fluid. Large fluctuations in total kinetic energy occur in this regime, with periodicities ranging from 40 to 1400Myr. The transition to thermal turbulence occurs in these calculations at Rayleigh numbers well below the value estimated for subsolidus convection in the mantle, suggesting thermally turbulent convection may occur in the mantle, a consequence of internal heat sources. Thermal turbulence offers an explanation for long-term fluctuations in the rate of subduction, sea-floor spreading and global volcanic activity.