Heat Flow Scaling for Mantle Convection with Continents and Preliminary Application to Continental Growth

To help understand the heat loss properties of the mantle/continent system, we develop a general scaling theory for thermal convection below insulating lids of finite lateral extent. The theory is based on a systems analogy that considers insulated and non-insulated regions to operate in parallel. Full numerical simulations of thermal convection beneath insulating lids are used to test the simplest form of the theory with good results. The theory is extended to consider two of the complexities specific to mantle convection: Strongly temperature-dependent viscosity and the efficient subduction of oceanic lithosphere. The extended theory predicts that, for certain parameter windows, a significant increase in the lateral extent of continents, i.e., an increase in the amount of insulation, can lead to a negligable change in global mantle heat loss. Even more contrary to simple intuition, the theory also predicts that parameter windows exist in which an increase in continental extent can lead to an increase in global mantle heat loss. These result are confirmed through numerical simulations of mantle convection that allow for plate-like behavior and include continental analogs. The amount of continental insulation that does not significantly damp global mantle heat loss is predicted to decrease as convective vigor in the mantle increases. This suggests that a theoretical continental growth curve can be constructed that allows mantle heat loss to remain at a near optimal level over geologic history. The robustness of this idea will be tested for a range of parameter conditions to determine if an optimal theory of continental growth may be applicable to Earth.