The structure of convection in the spherical mantle with internal heating

Abstract

Thermal convection in the mantle is caused by the heat transported upwards from the core and by the heat produced by the internal radioactive sources. According to the data on the heat transfer by the mantle plumes and geochemical evidence, only 20% of the total heat of the Earth is supplied to the mantle from the core, whereas most of the heat is generated by the internal sources. Along with the models that correctly allow for the internal heat sources, there are also many publications (including monographs) on the models of mantle convection that completely ignore the internal heating or the heat flux from below. In this study, we analyze to what extent these approximations could be correct. The analytical distributions of temperature and heat flux in the case of internal heating without convection and the results of the numerical modeling for convection with different intensity are presented. It is shown that the structure of thermal convection is governed by the distribution of the heat flux in the mantle but not by the heat balance, as it is typically implicitly assumed in most works. Heat production by the internal sources causes the growth of the heat flux as a function of radius. However, in the spherical mantle of the Earth, the heat flux decreases with radius due to the geometry. It turned out that with the parameters of the present Earth, both these effects compensate each other to a considerable extent, and the resulting heat flux turns out to be nearly constant as a function of radius. Since the structure of the convective flows in the mantle is determined by the distributions of heat flux and total heat flux, in the Cartesian models of the mantle convection the effective contribution of internal heating is small, and ignoring the heat flux from the core significantly distorts the structure of the convective currents and temperature distributions in the mantle.