Publication Date:
2013-11-04
Description:
We examined in an analytical manner the stability of thermal stratification of highly compressible fluids with depth-dependent physical properties, to obtain the fundamental insights into the convective motion in the mantles of ‘super-Earths’. We consider a stability in a horizontal layer of a highly compressible fluid, which is in a hydrostatic (motionless) state under a uniform gravitational field. As a model of pressure-dependence in material properties, we employed an exponential decrease in thermal expansivity and exponential increase in thermal conductivity with depth. By using the ‘parcel method’ as in meteorological studies, we investigated the change in the static stability of thermal stratification depending on the adiabatic compression as well as the depth-dependence of thermal expansivity and conductivity, with a special emphasis on the changes in the depth ranges (or the vertical extent) of unstable thermal stratifications. We found that a large thermal expansivity at depth tends to suppress the instability within the entire layer of compressible fluids, as opposed to the cases with incompressible ones. This means that the effect of adiabatic compression is of crucial importance in the understanding the mantle dynamics of super-Earths. We also found that, for the conditions relevant to super-Earths of 10 times mass of the Earth's, the stability of thermal stratification significantly varies. For example, the stratification is unstable in the entire layer only for a strong decrease in thermal expansivity with depth and/or low surface temperature. If this condition is not met, the fluid layer will be split into a ‘troposphere’ and ‘stratosphere’, depending on the stable or unstable thermal stratification. In addition, for the cases with extremely high surface temperature, a stratification can be stable even in the entire depth range of the fluid layer. The present findings may imply that the models of thermal evolution of super-Earths have to be carefully reconsidered by incorporating the effects of ‘stratosphere’ on the overall heat transfer within the planets.
Print ISSN:
0956-540X
Electronic ISSN:
1365-246X
Topics:
Geosciences
Published by
Oxford University Press
on behalf of
The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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