Utilizing cooling in Cartesian geometry systems to obtain the mean temperatures and convective planforms found in isoviscous spherical shell convection

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[5418] Planetary Sciences: Solid Surface Planets / Heat Flow, [8120] Tectonophysics / Dynamics Of Lithosphere And Mantle: General, [8121] Tectonophysics / Dynamics: Convection Currents, And Mantle Plumes, [8130] Tectonophysics / Heat Generation And Transport

Scientific paper

Cartesian convection systems feature higher mean temperatures than those found in spherical shell convection models. In this study, heat sinks are implemented to lower the mean temperature of vigorously convecting 3D Cartesian systems. We seek to identify the heating and cooling parameters in isoviscous Cartesian geometry calculations that will yield temperature profiles (geotherms) similar to those found in a spherical shell. We analyze the mean temperatures for convection in a spherical shell geometry from previously published results and derive a predictive equation for the mean temperature in a vigorously convecting fluid with a given nondimensional internal heating or cooling rate, H, Rayleigh number, Ra, and core to planet radii ratio, f. For the cases examined, we succeed in predicting the mean temperature for systems with different f to within about 3 percent. The effect of solution domain size on the convective planforms and temperature profiles is also considered. Systems featuring lower Rayleigh numbers (10^5-10^6) and internal heating rates (H=5) have temperatures and planforms that are more dependent on solution domain size. Our results show promise for improving the similarity of the mean temperatures and geotherms found in Cartesian systems and those observed in spherical shell convection. The findings are particularly relevant for modelling the computationally challenging high Rayleigh number convection predicted in super-Earth type exo-solar planets.

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