CONVECTION WITH INTERNAL HEAT-SOURCES AND THERMAL TURBULENCE IN THE EARTHS MANTLE

The influence of internal heat sources on mantle convection is investi gated using numerical calculations of 2-D thermal convection in an inf inite Prandtl number, incompressible fluid. The geometry is a cylindri cal annulus with inner and outer radii in proportion to the whole mant le. Time-dependent calculations are made starting from random initial conditions, with Rayleigh numbers Ra(T) (based on boundary-temperature difference) and Ra(H) (based on internal-heat production) in the rang e 10(3) less-than-or-equal-to Ra(T) less-than-or-equal-to 10(7) and 0 less-than-or-equal-to Ra(H) less-than-or-equal-to 24 Ra(T). At fixed R a(T), increasing Ra(H) results in transitions in flow structure from s teady cells, to a pattern of stationary cells with time-variable ampli tude, and finally to thermally turbulent convection with a non-station ary cell count. For Ra(T) < 10(5), the equilibrium cell-aspect ratio i ncreases with Ra(H), from near unity (10-cell solution) at Ra(H) = 0 t o three (four-cell solution) at Ra(H) = 8Ra(T). Above Ra(T) = 10(5), t he flow is fully time dependent and consists of unequal, non-stationar y cells separated by migrating boundaries. Recurring plumes develop fr om instabilities in both the surface and the basal boundary layers, tr avel with and modify the large-scale circulation. For Ra(T) > 10(5) an d Ra(H) > Ra(T) approximately, the travelling plumes disrupt the large -scale circulation, producing turbulent convection. At Ra(T) = 10(7) t he flow is fully developed thermal turbulence, and for Ra(H) > 0, cons ists of a rapidly fluctuating, irregular flow driven by transient risi ng and sinking sheets of buoyant fluid. Large fluctuations in total ki netic energy occur in this regime, with periodicities ranging from 40 to 1400 Myr. The transition to thermal turbulence occurs in these calc ulations at Rayleigh numbers well below the value estimated for subsol idus convection in the mantle, suggesting thermally turbulent convecti on may occur in the mantle, a consequence of internal heat sources. Th ermal turbulence offers an explanation for long-term fluctuations in t he rate of subduction, sea-floor spreading and global volcanic activit y.