Convection under a lid of finite conductivity: Heat flux scaling and application to continents

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Abstract
A scaling law for the heat flux out of a convective fluid covered totally or partially by a finitely conducting lid is proposed. This scaling is constructed in order to quantify the heat transfer out of the Earth's mantle, taking into account the effect of the dichotomy between oceans and continents, which imposes heterogeneous thermal boundary conditions at the surface of the mantle. The effect of these heterogeneous boundary conditions is studied here using simple two‐dimensional models, with the mantle represented by an isoviscous fluid heated from below and continents represented by nondeformable lids of finite thermal conductivity set above the surface of the model. We use free‐slip boundary conditions under the oceanic and continental zones in order to study in an isolated way the possible thermal effect of continents, independently of all mechanical effect. A systematic study of the heat transfer as a function of the Rayleigh number of the fluid, of the width of the lid, and of its thermal properties is carried out. We show that estimates of continental lithosphere thickness imply a strong insulating effect from continents on mantle heat loss, at least locally. The heat flux below continents was low in the past and of the order of the present one if the continental thickness has remained broadly constant over the Earth's history.

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