TURBULENT 3-D THERMAL-CONVECTION IN AN INFINITE PRANDTL NUMBER, VOLUMETRICALLY HEATED FLUID - IMPLICATIONS FOR MANTLE DYNAMICS

The structure and time dependence of 3-D thermal convection in a volum etrically heated, infinite Prandtl number fluid is examined for high v alues of the Rayleigh number. The methods employed allow the numerical experiments to proceed for long-enough times to derive good estimates of mean and fluctuating parts of the structure. An iterative multirig id method to solve for the buoyant, incompressible viscous flow at eac h time step of the energy equation is a novel aspect of the methodolog y. A simple explicit time step of the energy equation is utilized that vectorizes well on serial computers and which is ideally suited to ma ssively parallel computers. Numerical experiments were carried out for Rayleigh numbers from 3 x 10(6) to 3 x 10(7) in a cartesian region wi th a prescribed temperature at the top boundary and an adiabatic botto m boundary. Over this complete range of Rayleigh number, the flow stru cture consists dominantly of cold, nearly axisymmetric plumes that mig rate horizontally sweeping off the cold thermal-boundary layer that fo rms at the top of the convecting fluid. Plumes disappear by coalescing with other plumes; new plumes are created by thermal-boundary-layer i nstability. Sheet plumes form only occasionally and do not penetrate t o significant depths in the fluid. Plumes have sizes comparable to the thickness of the thermal-boundary layer and an average spacing compar able to the fluid depth. No persistent large-scale motion in the fluid can be identified. Its absence may reflect the large subadiabatic str atification that develops beneath the thermal-boundary layer as cold p lumes penetrate to the bottom boundary without thermally equilibrating with surrounding fluid. We consider the possible implications for con vection in planetary mantles and for the existence of plate tectonics.