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

Abstract

[1] 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.

Uncertainties in the composition of Earth, its core and silicate sphere

“…A current value for the radiogenic heat contribution is 21 TW (14 TW from the mantle and 7 TW from the continents), which, in turn, would imply a mantle Urey ratio of 0.3. This mantle Urey ratio is low and outside the range of most geophysical models that attempt to parameterize convection in the mantle (e.g., [15][16][17][18]). …”

Temperature and rheological properties of the mantle beneath the North American craton from an analysis of heat flux and seismic data

“…As explained in section 2.1, heating by mantle plumes is unlikely. Heat can also be brought to the lithosphere by underlying mantle that gets swept past it [Lenardic, 1997;Lenardic and Moresi, 2001;Grigné et al, 2007]. In this case, both the magnitude and lateral variation of the basal heat flux depend on the shape and depth of the lithospheric root, but the key question is whether smallscale convection gets suppressed by large-scale shear.…”

Comparative Experimental Study of Fixed Temperature and Fixed Heat Flux Boundary Conditions in Turbulent Thermal Convection

“…How the two different BCs will affect the flow dynamics and transport properties in convective turbulence is not only of fundamental interest, but is also crucial for understanding the convection phenomena occurring ubiquitously in nature (see, e.g. [6][7][8] and references therein). An idealized model for studying thermal turbulence is the turbulent RayleighBénard (RB) convection, a fluid layer heated from below and cooled from the top [9][10][11][12].…”