Turbulent 3‐D thermal convection in an infinite Prandtl number, volumetrically heated fluid: implications for mantle dynamics

SUMMARY The structure and time dependence of 3‐D thermal convection in a volumetrically heated, infinite Prandtl number fluid is examined for high values 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 multirigid method to solve for the buoyant, incompressible viscous flow at each time step of the energy equation is a novel aspect of the methodology. A simple explicit time step of the energy equation is utilized that vectorizes well on serial computers and which is ideally suited to massively parallel computers. Numerical experiments were carried out for Rayleigh numbers from 3 × 10 6 to 3 × 10 7 in a cartesian region with a prescribed temperature at the top boundary and an adiabatic bottom boundary. Over this complete range of Rayleigh number, the flow structure consists dominantly of cold, nearly axisymmetric plumes that migrate horizontally sweeping off the cold thermal‐boundary layer that forms at the top of the convecting fluid. Plumes disappear by coalescing with other plumes; new plumes are created by thermal‐boundary‐layer instability. Sheet plumes form only occasionally and do not penetrate to significant depths in the fluid. Plumes have sizes comparable to the thickness of the thermal‐boundary layer and an average spacing comparable to the fluid depth. No persistent large‐scale motion in the fluid can be identified. Its absence may reflect the large subadiabatic stratification that develops beneath the thermal‐boundary layer as cold plumes penetrate to the bottom boundary without thermally equilibrating with surrounding fluid. We consider the possible implications for convection in planetary mantles and for the existence of plate tectonics.