Thermal convection and the convective regime diagram in super-Earths

Abstract

Numerical models of bottom-heated thermal convection of highly compressible fluid with strongly temperature-dependent viscosity are presented to understand how the Rayleigh number Ra and the temperature dependence of viscosity exert control over the regimes of thermal convection in massive super-Earths. Thermodynamic properties of mantle materials are pressure dependent, but other material properties including the viscosity are not. A stagnant lid develops along the surface of the planet, when the viscosity contrast across the mantle due to temperature dependence r exceeds 10 6 at high Rayleigh number relevant to super-Earths. The threshold in r, which increases with increasing Ra, is higher than that expected for the Earth from earlier Boussinesq models. The efficiency of convective heat transport measured by the Nusselt number Nu is considerably lower than that expected from Boussinesq models; Nu depends on Ra and r as Nu = 59 Á r . Strong adiabatic compression significantly reduces the activity of hot ascending plumes especially at high r. At r relevant for super-Earths, hot ascending plumes lose their buoyancy on their way and hardly reach the surface boundary: hot spot volcanism due to ascending plumes is probably suppressed on super-Earths. The lithosphere is considerably thicker than that suggested by earlier Boussinesq models and is unlikely to show a plate-like behavior.

Extremely long transition phase of thermal convection in the mantle of massive super-Earths

“…These values are the same as the values for Case 5 in Table 1 of Miyagoshi et al (2015). Note that the free parameters are all defined with the surface values of material properties.…”

“…We present the potential temperature as in Tachinami et al (2014) and Miyagoshi et al (2015) because it is more relevant to mantle convection than the temperature itself. Temperature variation caused by adiabatic compression does not drive the mantle convection; nevertheless, it overshadows the potential temperature variation that drives the mantle convection at large Di values assumed here (Fig.…”

“…2). Whole layer convection is the convective flow pattern that we obtained as the statistical steady state in Miyagoshi et al (2015).…”

“…We assumed that the temperature is fixed at the bottom boundary; however, the temperature may decrease with time in super-Earths because of core cooling. Given the low efficiency of convective cooling of the compressible mantle of super-Earths found in Miyagoshi et al (2015), the amount of the temperature decrease is probably small and is unlikely to substantially affect the duration of the transient-layered convection.…”

“…For this purpose, we present an example of transient mantle convection we encountered in our numerical studies of a massive super-Earth to discuss how the nature of thermal convection can change in the course of its approach to the statistical steady state and on what timescale the change occurs (note that Miyagoshi et al (2015) reports only the convections in their statistical steady states).…”