Linear Analysis on the Onset of Thermal Convection of Highly Compressible Fluids: Implications for the Mantle Convection of Super-Earths

kameyama, masanori ; takehiro miyagoshi ; ogawa, masaki;

A series of linear analysis was performed on the onset of thermal convection of highly compressible fluids, in order to deepen the fundamental insights into the mantle convection of massive super-Earths in the presence of strong adiabatic compression. We consider the temporal evolution (growth or decay) of an infinitesimal perturbation superimposed to a highly compressible fluid which is in a hydrostatic (motionless) and conductive state in a basally heated horizontal layer. As a model of pressure-dependence in material properties, we employed an exponential decrease in thermal expansivity α and exponential increase in (reference) density ρ with depth. The linearized equations for conservation of mass, momentum and internal (thermal) energy are numerically solved for the critical Rayleigh number as well as the vertical profiles of eigen functions for infinite simalperturbations. The above calculations are repeatedly carried out by systematically varying (i) the dissipation number (Di), (ii) the temperature at the top surface and (iii) the magnitude of pressure-dependence in α and ρ. Our analysis demonstrated that the on set of the rmal convection is strongly affected by the adiabatic compression, in response to the changes in the static stability of thermal stratification in the fluidlayer. For sufficiently large Di where a thick sublayer of stables tratification develops in the layer, for example, the critical Rayleigh number explosively increases with Di, together with drastic decreases in the length scales of perturbations both in vertical and horizontal directions. In particular, for very large Di, a thick‘ stratosphere’ occurs in the fluid layer where the vertical motion is significantly suppressed, resulting in a shrink of the incipient convection in a thin sublayer of unstable thermals tratification. In addition, when Diexce edsathres hold value above which a thermal stratification becomes stable in the entire layer, no perturbation is allowed to grow with time regardless of the Rayleigh number and/or the horizontal wavelength. We also found that the effect of adiabatic compression becomes prominent for higher temperature at the top surface of the fluid layer. These findings may imply the crucial importance of adiabatic compression in understanding the dynamics and evolution of the mantles of massive super-Earths, particularly for those orbiting their parent stars very closely.